For any two sets A and B, (A − B) ∪ (B − A) = (a) \((A-B)\cup A\) (b) \((B-A)\cup B\) (c) \((A\cup B)-(A\cap B)\) (d) \((A\cup B)\cap(A\cap B)\) Solution By definition, \[ (A-B)\cup(B-A)=A\Delta B \] Also, \[ A\Delta B=(A\cup B)-(A\cap B) \] Therefore, \[ (A-B)\cup(B-A)=(A\cup B)-(A\cap B) \] Answer \[ \boxed{(A\cup B)-(A\cap B)} \] […]

The symmetric difference of A = {1, 2, 3} and B = {3, 4, 5} is (a) \(\{1,2\}\) (b) \(\{1,2,4,5\}\) (c) \(\{4,3\}\) (d) \(\{2,5,1,4,3\}\) Solution \[ A=\{1,2,3\}, \qquad B=\{3,4,5\} \] \[ A-B=\{1,2\} \] \[ B-A=\{4,5\} \] Symmetric difference: \[ A\Delta B=(A-B)\cup(B-A) \] \[ =\{1,2\}\cup\{4,5\} \] \[ =\{1,2,4,5\} \] Answer \[ \boxed{\{1,2,4,5\}} \] Correct option: (b)

“`html The symmetric difference of A and B is not equal to (a) \((A-B) \cap (B-A)\) (b) \((A-B) \cup (B-A)\) (c) \((A \cup B)-(A \cap B)\) (d) \(\{(A \cup B)-A\} \cup \{(A \cup B)-B\}\) Solution Symmetric difference is defined as \[ A \Delta B = (A-B)\cup(B-A) \] Also, \[ A \Delta B=(A\cup B)-(A\cap B) \]

If A = {1, 3, 5, B} and B = {2, 4}, then (a) \(4 \in A\) (b) \(\{4\} \subset A\) (c) \(B \subset A\) (d) none of these Solution Given, \[ A=\{1,3,5,B\} \] and \[ B=\{2,4\} \] Here, the set \(B\) itself is an element of \(A\), not the elements \(2\) and \(4\). Therefore,

For any two sets A and B, A ∩ (A ∪ B) = (a) \(A\) (b) \(B\) (c) \(\phi\) (d) none of these Solution Using absorption law, \[ A \cap (A \cup B)=A \] Answer \[ \boxed{A} \] Correct option: (a) Next Question / Full Exercise

The number of subsets of a set containing n elements is (a) \(n\) (b) \(2^n-1\) (c) \(n^2\) (d) \(2^n\) Solution If a set contains \(n\) elements, then each element has two choices: either included in a subset or not included in a subset Therefore, total number of subsets \[ =2 \times 2 \times 2 \cdots

Let A and B be two sets in the same universal set. Then, A − B = (a) \(A \cap B\) (b) \(A’ \cap B\) (c) \(A \cap B’\) (d) none of these Solution By definition, \[ A-B \] means the elements which belong to \(A\) but do not belong to \(B\). Therefore, \[ A-B=A

For any set A, (A′)′ is equal to (a) \(A’\) (b) \(A\) (c) \(\phi\) (d) none of these Solution By the double complement law, \[ (A’)’=A \] Hence, the complement of the complement of a set is the set itself. Answer \[ \boxed{A} \] Correct option: (b) Next Question / Full Exercise

If A and B are two finite sets such that n(A) > n(B) and the difference of the number of elements of the power sets of A and B is 96, then n(A) – n(B) =………….. Solution Let \[ n(A)=m,\qquad n(B)=n \] Number of elements in power sets: \[ n(P(A))=2^m,\qquad n(P(B))=2^n \] Given, \[ 2^m-2^n=96

For any two sets A and B, if n(A) = 15, n(B) = 12, A∩B = Φ and B⊄A, then the maximum and minimum possible values of n(A∆B) are………..and………….respectively. Solution Given, \[ A \cap B = \Phi \] Therefore, \[ A \Delta B = A \cup B \] Hence, \[ n(A \Delta B)=n(A)+n(B) \] \[