Let `A_(1)`, `A_(2)` and `A_(3)` be subsets of a set `X`. Which one of the following is correct ?

Let `A_(1)`, `A_(2)` and `A_(3)` be subsets of a set `X`. Which one of the following is correct ?
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Let `A_(1)`, `A_(2)` and `A_(3)` be subsets of a set `X`. Which one of the following is correct ? A. ... (3)` only if `A_(2)=A_(3)` D. None of these
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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 = {(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.

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 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 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

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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.

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.

Let Pi and Pj be two processes, R be the set of variables read from memory, and W be the set of variables written to memory. For the concurrent execution of two processes Pi and Pj, which of the following conditions is not true? (A) R(Pi)∩W(Pj)=Φ (B) W(Pi)∩R(Pj)=Φ (C) R(Pi)∩R(Pj)=Φ (D) W(Pi)∩W(Pj)=Φ

Description : Let Pi and Pj be two processes, R be the set of variables read from memory, and W be the set of variables written to memory. For the concurrent execution of two processes Pi and Pj, which of the following conditions is not true? (A) R(Pi)∩W(Pj)=Φ (B) W(Pi)∩R(Pj)=Φ (C) R(Pi)∩R(Pj)=Φ (D) W(Pi)∩W(Pj)=Φ

Last Answer : (C) R(Pi)∩R(Pj)=Φ 

Let P(m,n) be the statement “m divides n” where the Universe of discourse for both the variables is the set of positive integers. Determine the truth values of the following propositions. (a) ∃m ∀n P(m,n) (b) ∀n P(1,n) (c) ∀m ∀n P(m,n) (A) (a)-True; (b)-True; (c)-False (B) (a)-True; (b)-False; (c)-False (C) (a)-False; (b)-False; (c)-False (D) (a)-True; (b)-True; (c)-True

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Let A and B be sets in a finite universal set U. Given the following: |A – B|, |AÅB|, |A|+|B| and |AÈB| Which of the following is in order of increasing size ? (A) |A – B| ≤ |AÅB| ≤ |A| + |B| ≤ |AÈB| (B) |AÅB| ≤ |A – B| ≤ |AÈB| ≤ |A| + |B| (C) |AÅB| ≤ |A| + |B| ≤ |A – B| ≤ |AÈB| (D) |A – B| ≤ |AÅB| ≤ |AÈB| ≤ |A| + |B|

Description : Let A and B be sets in a finite universal set U. Given the following: |A - B|, |AÅB|, |A|+|B| and |AÈB| Which of the following is in order of increasing size ? (A) |A - B| ≤ |AÅB| ≤ |A| + |B| ≤ |AÈB| (B) |AÅB| ≤ |A ... |AÅB| ≤ |A| + |B| ≤ |A - B| ≤ |AÈB| (D) |A - B| ≤ |AÅB| ≤ |AÈB| ≤ |A| + |B|

Last Answer : (D) |A – B| ≤ |AÅB| ≤ |AÈB| ≤ |A| + |B|