If a relation `R` on the set `N` of natural numbers is defined as `(x,y)hArrx^(2)-4xy+3y^(2)=0,Aax,yepsilonN`. Then the relation `R` is

If a relation `R` on the set `N` of natural numbers is defined as `(x,y)hArrx^(2)-4xy+3y^(2)=0,Aax,yepsilonN`. Then the relation `R` is
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If a relation `R` on the set `N` of natural numbers is defined as `(x,y)hArrx^(2) ... symmetric B. reflexive C. transitive D. an equivalence relation.
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On a set N of all natural numbers is defined the relation R by a R b iff the GCD of a and b is 2, then R is -Maths 9th

Description : On a set N of all natural numbers is defined the relation R by a R b iff the GCD of a and b is 2, then R is -Maths 9th

Last Answer : (c) Symmetric only Let a ∈N. Then (a, a) ∉R as the GCD of a' and a' is a' not 2. R is not reflexive Let a, b ∈N. Then, (a, b) ∉R ⇒ GCD of a' and b' is 2 ⇒ GCD of b' and a' is 2 ⇒ (b, a) ∈R ∴ R ... , let a = 4, b = 10, c = 12 GCD of (4, 10) = 2 GCD of (10, 12) = 2 But GCD of (4, 12) = 4.

If R is a relation defined on the set of natural numbers N such that (a, b) R (c, d) if and only if a + d = b + c, then R is -Maths 9th

Description : If R is a relation defined on the set of natural numbers N such that (a, b) R (c, d) if and only if a + d = b + c, then R is -Maths 9th

Last Answer : (d) An equivalence relationWe can check the given properties as follows: Reflexive: Let (a, b) ∈ N x N. Then (a, b) ∈ N ⇒ a + b = b + a (Communtative law of Addition) ⇒ (a, b) R (b, a) ⇒ (a, b) R (a, ... , f) ⇒ (a, b) R (e, f) on N x N so R is transitive.Hence R is an equivalence relation on N N.

Let R be a relation on the set N, defined by {(x, y) : 2x – y = 10} then R is -Maths 9th

Description : Let R be a relation on the set N, defined by {(x, y) : 2x – y = 10} then R is -Maths 9th

Last Answer : (a) ReflexiveGiven, {(\(x\), y) : 2\(x\) – y = 10} Reflexive, \(x\) R \(x\) = 2\(x\) – \(x\) = 10 ⇒ \(x\) = 10 ⇒ y = 10 ∴ Point (10, 10) ∈ N ⇒ R is reflexive.

If `y=(sinx+cos e cx)^2+(cosx+secx)^2` , then the minimum value of `y ,AAx in R ,` 7 (b) 3 (c) 9 (d) 0

Description : If `y=(sinx+cos e cx)^2+(cosx+secx)^2` , then the minimum value of `y ,AAx in R ,` 7 (b) 3 (c) 9 (d) 0

Last Answer : If `y=(sinx+cos e cx)^2+(cosx+secx)^2` , then the minimum value of `y ,AAx in R ,` 7 (b) 3 (c) 9 (d) 0 A. 7 B. 8 C. 9 D. 11

On the set R of all real numbers, a relation R is defined by R = {(a, b) : 1 + ab > 0}. Then R is -Maths 9th

Description : On the set R of all real numbers, a relation R is defined by R = {(a, b) : 1 + ab > 0}. Then R is -Maths 9th

Last Answer : (a) Reflexive and symmetric only(a, a) ∈ R ⇒ 1 + a . a = 1 + a2 > 0 V real numbers a ⇒ R is reflexive (a, b) ∈ R ⇒ 1 + ab > 0 ⇒ 1 + ba > 0 ⇒ (b, a) ∈ R ⇒ R is symmetricWe observe that \(\big(1,rac{1}{2}\big) ... }{2},-1\big)\) ∈ Rbut (1, - 1) ∉ R as 1 + 1 (-1) = 0 \( ot>\) 0 ⇒ R is not transitive.

Let N be the set of natural numbers. Describe the following relation in words giving its domain -Maths 9th

Description : Let N be the set of natural numbers. Describe the following relation in words giving its domain -Maths 9th

Last Answer : The given relation stated in words is R = {(x, y) : x is the fourth power of y; x ∈ N, y ∈ {1, 2, 3, 4}}.

Let R be a relation defined on the set A of all triangles such that R = {(T1, T2) : T1 is similar to T2}. Then R is -Maths 9th

Description : Let R be a relation defined on the set A of all triangles such that R = {(T1, T2) : T1 is similar to T2}. Then R is -Maths 9th

Last Answer : (d) An equivalence relation.Every triangle is similar to itself, so (T1, T1) ∈ R ⇒ R is reflexive. (T1, T2) ∈ R ⇒ T1 ~ T2 ⇒T2 ~ T1, ⇒ (T2, T1) ∈ R ⇒ R is symmetrictransitive. ∴ R is an equivalence relation.

Let A = {1, 2, 3, 4}, B = {5, 6, 7, 8}. Then R = {(1, 5), (1, 7), (2, 6)} is a relation from set A to B defined as : -Maths 9th

Description : Let A = {1, 2, 3, 4}, B = {5, 6, 7, 8}. Then R = {(1, 5), (1, 7), (2, 6)} is a relation from set A to B defined as : -Maths 9th

Last Answer : (d) R = {(a, b) : b/a is odd} Since (2, 6) ∈R, the relation a and b are odd does not exist. Since (1, 5) and (1, 7) ∈R, the relation a and b are even does not exist. None of the ... \(rac{7}{1}\) = 7, \(rac{6}{2}\) = 3, quotients being all odd numbers, the relation b/a is odd exists.

If `X""=""{4^n-3n-1"":""n in N}""a n d""Y""=""{9(n-1)"": n in N}` , where N is the set of natural numbers, then `XuuY` is equal to (1) N (2) Y - X (3)

Description : If `X""=""{4^n-3n-1"":""n in N}""a n d""Y""=""{9(n-1)"": n in N}` , where N is the set of natural numbers, then `XuuY` is equal to (1) N (2) Y - X (3)

Last Answer : If `X""=""{4^n-3n-1"":""n in N}""a n d""Y""=""{9(n-1)"": n in N}` , where N is the set of natural numbers ... 3) X (4) Y A. `X` B. `Y` C. `N` D. `Y-X`

Find the value of 4x2 + y2 + 25z2 + 4xy – 10yz – 20zx when x = 4, y = 3 and z = 2. -Maths 9th

Description : Find the value of 4x2 + y2 + 25z2 + 4xy – 10yz – 20zx when x = 4, y = 3 and z = 2. -Maths 9th

Last Answer : 4x²+y²+25z²+4xy-10yz-20zx when x=4, y=3 &z=2 so =>4(4)²+(3)²+ 25(2)²+4(4)(3)-10(3)(2)-20(2)(4) =>64+9+100+48-60-160 =>221-220 =>1

Let `0le theta le pi/2` `x=Xcos theta + Ysin theta` `y=Xsin theta - Y cos theta` such that `x^2+4xy+y^2=aX^2+bY^2` where `a,b` are constants such that

Description : Let `0le theta le pi/2` `x=Xcos theta + Ysin theta` `y=Xsin theta - Y cos theta` such that `x^2+4xy+y^2=aX^2+bY^2` where `a,b` are constants such that

Last Answer : Let `0le theta le pi/2` `x=Xcos theta + Ysin theta` `y=Xsin theta - Y cos theta` such that `x^2+4xy+y^2=aX^2+ ... C. `a=3`, `b=-1` D. `theta=(pi)/(3)`

Let R be a relation from A = {1, 2, 3, 4, 5, 6} to B = {1, 3, 5} which is defined as “x is less than y”. -Maths 9th

Description : Let R be a relation from A = {1, 2, 3, 4, 5, 6} to B = {1, 3, 5} which is defined as “x is less than y”. -Maths 9th

Last Answer : R = {a, b : a < b, a ∈ A, b ∈ B}, where A = {1, 2, 3, 4, 5, 6} and B = {1, 3, 5}. ∴ R = {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)} Domain of R = {1, 2, 3, 4} Range of R = {3, 5} Codomain of R = {1, 3, 5}.

If R is a relation in N × N defined by (a, b) R (c, d) if and only if ad = bc, show that R is an equivalence relation. -Maths 9th

Description : If R is a relation in N × N defined by (a, b) R (c, d) if and only if ad = bc, show that R is an equivalence relation. -Maths 9th

Last Answer : (i) R is reflexive. For all (a, b) ∈ N N we have (a, b) R (a, b) because ab = ba ⇒ R is reflexive. (ii) R is symmetric. Suppose (a, b) R (c, d) Then (a, b) R (c, d) ⇒ ... ) R (e, f) ⇒ R is transitive. Since R is reflexive, symmetric and transitive, therefore, R is an equivalence relation on N N.

Let R and S be two fuzzy relations defined as: Image Then, the resulting relation, T, which relates elements of universe x to elements of universe z using max-min composition is given by

Description : Let R and S be two fuzzy relations defined as: Then, the resulting relation, T, which relates elements of universe x to elements of universe z using max-min composition is given by

Last Answer : Answer: C

Let R be a relation defined as a Rb if | a – b | > 0, then the relation is -Maths 9th

Description : Let R be a relation defined as a Rb if | a – b | > 0, then the relation is -Maths 9th

Last Answer : (d) Symmetric and transitive| a - a | = | 0 | = 0 so (a, a) ∉R ⇒ R is not reflexive(a, b) ∈ R ⇒ | a - b | > 0 ⇒ | b - a | > 0 ⇒ (b, a) ∈R (∵ | a - b | = | b - a |) ⇒ R is symmetric (a, b) ∈ R ... a, b, c. ∴ | a - b | > 0 and | b - c | > 0 ⇒ | a - c | > 0 ⇒ (a, c) ∈ R ⇒ R is transitive.

Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is reflexive, symmetric or transitive. -Maths 9th

Description : Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is reflexive, symmetric or transitive. -Maths 9th

Last Answer : Reflexive: R = {(a, b) : b = a +1} = {(a, a + l) : a, a + 1∈{l, 2, 3, 4, 5, 6}} = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)} ⇒ R is not reflexive since (a, a) ∉R for all a. Symmetric: R is not symmetric as (a ... as (a, b) ∈ R and (b, c) ∈ R but (a, c) ∉ R e.g., (1, 2) ∈ R (2, 3) ∈ R but (1, 3) ∉R

Find the curl of the vector A = yz i + 4xy j + y k a) xi + j + (4y – z)k b) xi + yj + (z – 4y)k c) i + j + (4y – z)k d) i + yj + (4y – z)k

Description : Find the curl of the vector A = yz i + 4xy j + y k a) xi + j + (4y – z)k b) xi + yj + (z – 4y)k c) i + j + (4y – z)k d) i + yj + (4y – z)k

Last Answer : d) i + yj + (4y – z)k

If R is a relation on a finite set A having n elements, then the number of relations on A is -Maths 9th

Description : If R is a relation on a finite set A having n elements, then the number of relations on A is -Maths 9th

Last Answer : (d) \(2^{n^2}\)Set A has n elements ⇒ n(A) = n ⇒ A × A has n × n = n2 elements ∴ Number of relations on A = Number of subsets of A × A = \(2^{n^2}\)

If 2x^2 – 7xy + 3y^2 = 0, then the value of x : y is -Maths 9th

Description : If 2x^2 – 7xy + 3y^2 = 0, then the value of x : y is -Maths 9th

Last Answer : answer:

Let A = {(2, 5, 11)}, B = {3, 6, 10} and R be a relation from A to B defined by R = {(a, b) : a and b are co-prime}. Then R is -Maths 9th

Description : Let A = {(2, 5, 11)}, B = {3, 6, 10} and R be a relation from A to B defined by R = {(a, b) : a and b are co-prime}. Then R is -Maths 9th

Last Answer : (c) {(2, 3), (5, 3), (5, 6), (11, 3), (11, 6), (11, 10)}

Show that the relation R in the set A of all the books in a library of a school given by R = {(x, y): x and -Maths 9th

Description : Show that the relation R in the set A of all the books in a library of a school given by R = {(x, y): x and -Maths 9th

Last Answer : Given: A = {All books in a library of a school} R = {(x, y): x and y have the same number of pages} Reflexivity: (x, x) ∈ R ⇒ R is reflexive on A Symmetric: Since books x and y have the same number of pages ... and (y, z) ∈ R ⇒ (x, z) ∈ R ⇒ R is transitive on A. Hence, R is an equivalence relation.

The relation ‘is less than’ on a set of natural numbers is -Maths 9th

Description : The relation ‘is less than’ on a set of natural numbers is -Maths 9th

Last Answer : (c) Only transitiveLet N be the set of natural numbers. Then R = {(a, b) : a < b, a, b ∈N}A natural number is not less than itself ⇒ (a, a)∉R where a ∈N ⇒ R is not reflexive V a, b ∈N, (a, b) ∈R ⇒ a < b \( ot\ ... ∈N, (a, b) ∈R and (b, c) ∈R ⇒ a < b and b < c ⇒ a < c (a, c) ∈R ⇒ R is transitive.

if `x:y=2:5` then `(10x+3y):(5x+2y)` is _____.

Description : if `x:y=2:5` then `(10x+3y):(5x+2y)` is _____.

Last Answer : if `x:y=2:5` then `(10x+3y):(5x+2y)` is _____.

If ` X = 3Y = 4Z," then "X : Y : Z` = __________ .

Description : If ` X = 3Y = 4Z," then "X : Y : Z` = __________ .

Last Answer : If ` X = 3Y = 4Z," then "X : Y : Z` = __________ .

If the points (2, 1) and (1, – 2) are equidistant from the point (x, y), show that x + 3y = 0. -Maths 9th

Description : If the points (2, 1) and (1, – 2) are equidistant from the point (x, y), show that x + 3y = 0. -Maths 9th

Last Answer : (a) The distance d between any two points say P(x1, y1) and Q(x2, y2) is given by:d = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)⇒ d2 = (x2 - x1)2 + (y2 - y1)2 ⇒ d = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)( ... distance of a point P(x1, y1) form the origin= \(\sqrt{(x_2-0)^2+(y_2-0)^2}\) = \(\sqrt{x^2_1+y^2_1}\)

30. Radical centre of circles drawn on the sides as a diameter of triangle formed by the lines the `3x-4y+6=0`, `x-y+2=0` and `4x+3y-17=0` is

Description : 30. Radical centre of circles drawn on the sides as a diameter of triangle formed by the lines the `3x-4y+6=0`, `x-y+2=0` and `4x+3y-17=0` is

Last Answer : 30. Radical centre of circles drawn on the sides as a diameter of triangle formed by the lines the `3x-4y+6=0`, `x-y+ ... . (-2,3) C. (-2,-3) D. (2,3)

A pair of linear equations which has a unique solution x = 2, y = -3 is (a) x + y = -1 ; 2x – 3y = -5 (b) 2x + 5y = -11 ; 4x + 10y = -22(c) 2x – y = 1 ; 3x + 2y = 0 (d) x – 4y – 14 = 0 ;5x – y – 13 = 0

Description : A pair of linear equations which has a unique solution x = 2, y = -3 is (a) x + y = -1 ; 2x – 3y = -5 (b) 2x + 5y = -11 ; 4x + 10y = -22(c) 2x – y = 1 ; 3x + 2y = 0 (d) x – 4y – 14 = 0 ;5x – y – 13 = 0

Last Answer : (d) x – 4y – 14 = 0 ;5x – y – 13 = 0

I. 3x^2 – 47x + 184 = 0 II. 3y^2 – 38y + 119 = 0 1 : if x ≥ y 2 : if x ≤ y 3 : if x > y 4 : if x < y 5 : if x = y or relationship cannot be established

Description : I. 3x^2 – 47x + 184 = 0 II. 3y^2 – 38y + 119 = 0 1 : if x ≥ y 2 : if x ≤ y 3 : if x > y 4 : if x < y 5 : if x = y or relationship cannot be established

Last Answer : 3 : if x > y

Is 4xy plus 2y9 a linear equation?

Description : Is 4xy plus 2y9 a linear equation?

Last Answer : Without an equality sign the given expression is not anequation

For any two real number a b and , we defined aRb if and only if sin^2a + cos^2b = 1. The relation R is -Maths 9th

Description : For any two real number a b and , we defined aRb if and only if sin^2a + cos^2b = 1. The relation R is -Maths 9th

Last Answer : (d) an equivalence relationGiven, a R b ⇒ sin2a + cos2b = 1 Reflexive: a R a ⇒ sin2 a + cos2 a = 1 ∀ a ∈ R (True) Symmetric: a R b ⇒ sin2 a + cos2 b = 1 ⇒ 1 - cos2 a + 1 - sin2 b = 1 ⇒ sin2 b + ... + cos2 b + sin2 b + cos2 c = 2 ⇒ sin2 a + cos2 c = 1 ⇒ a R c (True)∴ R is an equivalence relation.

Let R be a relation on the set of integers given by a = 2^k .b for some integer k. Then R is -Maths 9th

Description : Let R be a relation on the set of integers given by a = 2^k .b for some integer k. Then R is -Maths 9th

Last Answer : (c) equivalence relationGiven, a R b = a = 2k .b for some integer. Reflexive: a R a ⇒ a = 20.a for k = 0 (an integer). True Symmetric: a R b ⇒ a = 2k b ⇒ b = 2-k . a ⇒ b R a as k, -k are both ... = 2k1 + k2 c, k1 + k2 is an integer. ∴ a R b, b R c ⇒ a R c True ∴ R is an equivalence relation.

Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then R is -Maths 9th

Description : Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then R is -Maths 9th

Last Answer : (b) Reflexive and transitive but not symmetricLet A = {1, 2, 3, 4} • ∵ (1, 1), (2, 2), (3, 3) and (4, 4) ∈R ⇒ R is reflexive • ∵ (1, 2) ∈ R but (2, 1) ∉ R ; (1, 3) ∈ R and (3, 1) ∉ R ; (3, 2) ∈R and (2, 3) ∉ R ⇒ R is not symmetric • (1, 3) ∈ R and (3, 2) ∈ R and (1, 2) ∈ R ⇒ R is transitive.

If 2x-y=4 then calculate 6x-3y=? (a)15 (b)12 (c)18 (d)10

Description : If 2x-y=4 then calculate 6x-3y=? (a)15 (b)12 (c)18 (d)10

Last Answer : (b)12

Which of the following is an equivalence relation defined on set A = {1, 2, 3} -Maths 9th

Description : Which of the following is an equivalence relation defined on set A = {1, 2, 3} -Maths 9th

Last Answer : (c) {(1, 1), (2, 2), (3, 1), (1, 3), (3, 3)} Option (c) satisfies all the conditions of an equivalence relation. (1, 1), (2, 2), (3, 3) ∈ R ⇒ (a, a) ∈ R V a ∈ A ⇒ R is reflexive (3, 1) ∈ R and (1, 3) ∈ R ... R and (1, 1) ∈ R ⇒ (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R V a, b, c ∈ A ⇒ R is transitive.

x^4 + xy^3 + x^3y + xz^3 + y^4 + yz^3 is divisible by : -Maths 9th

Description : x^4 + xy^3 + x^3y + xz^3 + y^4 + yz^3 is divisible by : -Maths 9th

Last Answer : answer:

If P, Y and Z are the weights of cement, fine aggregates and coarse aggregates respectively and W/C is the water cement ratio, the minimum quantity of water to be added to first batch, is obtained by the equation (A) 0.1P + 0.3Y + 0.1Z = W/C × P (B) 0.3P + 0.1Y + 0.01Z = W/C × P (C) 0.4P + 0.2Y + 0.01Z = W/C × P (D) 0.5P + 0.3Y + 0.01Z = W/C × P

Description : If P, Y and Z are the weights of cement, fine aggregates and coarse aggregates respectively and W/C is the water cement ratio, the minimum quantity of water to be added to first batch, is obtained by the equation (A) 0.1P + 0.3Y + 0. ... + 0.2Y + 0.01Z = W/C P (D) 0.5P + 0.3Y + 0.01Z = W/C P

Last Answer : Answer: Option B

If the roots of the equation x^2 + x + 1 = 0 are in the ratio of m : n, then which one of the following relation holds ? -Maths 9th

Description : If the roots of the equation x^2 + x + 1 = 0 are in the ratio of m : n, then which one of the following relation holds ? -Maths 9th

Last Answer : answer:

Suppose ORACLE relation R(A, B) currently has tuples {(1, 2), (1, 3), (3, 4)} and relation S(B, C) currently has {(2, 5), (4, 6), (7, 8)}. Consider the following two SQL queries SQ1 and SQ2 : SQ1 : Select * From R Full Join S On R.B=S.B; SQ2 : Select * From R Inner Join S On R.B=S.B; The numbers of tuples in the result of the SQL query SQ1 and the SQL query SQ2 are given by : (A) 2 and 6 respectively (B) 6 and 2 respectively (C) 2 and 4 respectively (D) 4 and 2 respectively

Description : Suppose ORACLE relation R(A, B) currently has tuples {(1, 2), (1, 3), (3, 4)} and relation S(B, C) currently has {(2, 5), (4, 6), (7, 8)}. Consider the following two SQL queries SQ1 and SQ2 ... (A) 2 and 6 respectively (B) 6 and 2 respectively (C) 2 and 4 respectively (D) 4 and 2 respectively

Last Answer : (D) 4 and 2 respectively

Let `S={x in R: x ge 0 and 2|(sqrt(x)-3|+sqrt(x)(sqrt(x)-6)+6=0}` then S (1) is an empty set (2) contains exactly one element (3) contains exact;y two

Description : Let `S={x in R: x ge 0 and 2|(sqrt(x)-3|+sqrt(x)(sqrt(x)-6)+6=0}` then S (1) is an empty set (2) contains exactly one element (3) contains exact;y two

Last Answer : Let `S={x in R: x ge 0 and 2|(sqrt(x)-3|+sqrt(x)(sqrt(x)-6)+6=0}` then S ... four elements C. is an empty set. D. contains exactly one elements

Let `S={x in R: x ge 0 and 2|(sqrt(x)-3|+sqrt(x)(sqrt(x)-6)+6=0}` then S (1) is an empty set (2) contains exactly one element (3) contains exact;y two

Description : Let `S={x in R: x ge 0 and 2|(sqrt(x)-3|+sqrt(x)(sqrt(x)-6)+6=0}` then S (1) is an empty set (2) contains exactly one element (3) contains exact;y two

Last Answer : Let `S={x in R: x ge 0 and 2|(sqrt(x)-3|+sqrt(x)(sqrt(x)-6)+6=0}` then S ... four elements C. is an empty set. D. contains exactly one elements

pH is defined as the negative logarithm of the hydrogen ion concentration. Comparing a pH 5 and a pH 8 solution, which of the following is true? w) There are 1,000 times more hydrogen ions in the pH 8 solution. x) There are 1,000 times more hydrogen ions in the pH 5 solution. y) There are 3 times more hydrogen ions in the pH 8 solution. z) Cannot tell the difference between these two solutions by pH, since the numbers are so close.

Description : pH is defined as the negative logarithm of the hydrogen ion concentration. Comparing a pH 5 and a pH 8 solution, which of the following is true? w) There are 1,000 times more hydrogen ions in ... . z) Cannot tell the difference between these two solutions by pH, since the numbers are so close.

Last Answer : ANSWER: X -- THERE ARE 1,000 TIMES MORE HYDROGEN IONS IN THE PH 5 SOLUTION

If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is -Maths 9th

Description : If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is -Maths 9th

Last Answer : (a) Since, (2, 0) is a solution of the given linear equation 2x + 3y = k, then put x =2 and y= 0 in the equation. ⇒ 2 (2) + 3 (0) = k ⇒ k = 4 Hence, the value of k is 4.

If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is -Maths 9th

Description : If (2, 0) is a solution of the linear equation 2x + 3y = k, then the value of k is -Maths 9th

Last Answer : (a) Since, (2, 0) is a solution of the given linear equation 2x + 3y = k, then put x =2 and y= 0 in the equation. ⇒ 2 (2) + 3 (0) = k ⇒ k = 4 Hence, the value of k is 4.

The height of h(A) of a fuzzy set A is defined as h(A) = sup A(x) xϵA Then the fuzzy set A is called normal when (A) h(A) = 0 (B) h(A) < 0 (C) h(A) = 1 (D) h(A) < 1

Description : The height of h(A) of a fuzzy set A is defined as h(A) = sup A(x)  xϵA Then the fuzzy set A is called normal when (A) h(A) = 0 (B) h(A) < 0 (C) h(A) = 1 (D) h(A) < 1

Last Answer : (C) h(A) = 1 

Choose the correct option. The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on a set A = {1, 2, 3} is -Maths 9th

Description : Choose the correct option. The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on a set A = {1, 2, 3} is -Maths 9th

Last Answer : R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3}. (i) Since (1, 1), (2, 2), (3, 3) ∈ R ⇒ R is reflexive. (ii) (1, 2) ∈ R but (2, 1) ∉ R ⇒ R is not symmetric. (iii) (1, 2) ∈ R, (2, 3) ∈ R and (1, 3) ∈R ⇒ R is transitive. ∴ Option (a) is the right answer.

The relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is: -Maths 9th

Description : The relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is: -Maths 9th

Last Answer : (c) Symmetric onlyAs (1, 1), (2, 2) ∉ R so R is not reflexive. A relation a R b is said to symmetric if (a, b) ∈ R ⇒ (b, a) ∈ R. Here (1, 2) ∈ R and (2, 1) ∈ R so it is symmetric. Also, as (1, 2) ∈ R, but (2, 3), (1, 3) ∉ R, so R is not transitive.

Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 12), (3, 6)} be a relation on set A = {3, 6, 9, 12}. The relation is -Maths 9th

Description : Let R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 12), (3, 6)} be a relation on set A = {3, 6, 9, 12}. The relation is -Maths 9th

Last Answer : (c) Reflexive and transitive onlyHere A = {3, 6, 9, 12} and R = {(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 12), (3, 6)} ∵ (3, 3), (6, 6), (9, 9), (12, 12) all belong to R ⇒ {(a, a): ∈R V a ∈A} ... 12) ∈ R and (3,12) ∈ R ⇒ (3, 12) ∈ R (x, y) ∈ R, (y, z) ∈ R ⇒ (x, z) ∈ R Hence R is transitive.

Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, -Maths 9th

Description : Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, -Maths 9th

Last Answer : (d) 7A = {1, 2, 3}. R = {(1, 2), (2, 3)} To make R an equivalence relation, it should be: (i) Reflexive: So three more ordered pairs (1, 1), (2, 2), (3, 3) should be added to R to make it ... 2, 1), (3, 2), (1, 3), (3, 1)} is an equivalence relation. So minimum 7 ordered pairs are to be added.

A relation R={A,B,C,D,E,F,G} is given with following set of functional dependencies: F={AD→E, BE→F, B→C, AF→G} Which of the following is a candidate key? (A) A (B) AB (C) ABC (D) ABD

Description : A relation R={A,B,C,D,E,F,G} is given with following set of functional dependencies: F={AD→E, BE→F, B→C, AF→G} Which of the following is a candidate key? (A) A (B) AB (C) ABC (D) ABD

Last Answer : Answer: D