May 2026

Verify A∪(B∩C) = (A∪B)∩(A∪C) Verify A∪(B∩C) = (A∪B)∩(A∪C) Question: Let \[ A=\{1,2,4,5\},\quad B=\{2,3,5,6\},\quad C=\{4,5,6,7\} \] Verify the identity: \[ A\cup(B\cap C)=(A\cup B)\cap(A\cup C) \] Solution First find \( B\cap C \): \[ B\cap C=\{5,6\} \] Now find \( A\cup(B\cap C) \): \[ A\cup(B\cap C) = \{1,2,4,5\}\cup\{5,6\} \] \[ A\cup(B\cap C)=\{1,2,4,5,6\} \] Now find \( A\cup […]

Verify A∩(B∪C) = (A∩B)∪(A∩C) Verify A∩(B∪C) = (A∩B)∪(A∩C) Question: Let \[ A=\{1,2,4,5\},\quad B=\{2,3,5,6\},\quad C=\{4,5,6,7\} \] Verify the identity: \[ A\cap(B\cup C)=(A\cap B)\cup(A\cap C) \] Solution First find \( B\cup C \): \[ B\cup C=\{2,3,4,5,6,7\} \] Now find \( A\cap(B\cup C) \): \[ A\cap(B\cup C) = \{1,2,4,5\}\cap\{2,3,4,5,6,7\} \] \[ A\cap(B\cup C)=\{2,4,5\} \] Now find \( A\cap

Verify De Morgan’s Laws for Sets A and B | Sets Class 11 Maths Verify De Morgan’s Laws for Sets A and B Let \[ U=\{1,2,3,4,5,6,7,8,9\} \] \[ A=\{2,4,6,8\} \] \[ B=\{2,3,5,7\} \] Verify that: (i) \[ (A \cup B)’=A’ \cap B’ \] (ii) \[ (A \cap B)’=A’ \cup B’ \] Solution (i) \[ A

Find the Smallest Set A Such That A ∪ {1, 2} = {1, 2, 3, 5, 9} Find the Smallest Set A Such That A ∪ {1, 2} = {1, 2, 3, 5, 9} Question: Find the smallest set \( A \) such that \[ A \cup \{1, 2\} = \{1, 2, 3, 5, 9\}

Find Complements of Sets A, B and C | Sets Class 11 Maths Find Complements of Sets A, B and C Let \[ U=\{1,2,3,4,5,6,7,8,9\} \] \[ A=\{1,2,3,4\} \] \[ B=\{2,4,6,8\} \] \[ C=\{3,4,5,6\} \] Find: (i) \(A’\) (ii) \(B’\) (iii) \((A \cap C)’\) (iv) \((A \cup B)’\) (v) \((A’)’\) (vi) \((B-C)’\) Solution (i) \[ A’=\{5,6,7,8,9\}

Find Difference of Sets A, B, C and D | Sets Class 11 Maths Find Difference of Sets A, B, C and D Let \[ A=\{3,6,12,15,18,21\} \] \[ B=\{4,8,12,16,20\} \] \[ C=\{2,4,6,8,10,12,14,16\} \] \[ D=\{5,10,15,20\} \] Find: (i) \(A-B\) (ii) \(A-C\) (iii) \(A-D\) (iv) \(B-A\) (v) \(C-A\) (vi) \(D-A\) (vii) \(B-C\) (viii) \(B-D\) Solution (i)

Find Intersections of Sets A, B, C and D | Sets Class 11 Maths Find Intersections of Sets A, B, C and D Let \[ A=\{x:x \in N\} \] \[ B=\{x:x=2n,\ n \in N\} \] \[ C=\{x:x=2n-1,\ n \in N\} \] \[ D=\{x:x \text{ is a prime natural number}\} \] Find: (i) \(A \cap B\)

Find Union and Intersection of Sets A, B, C and D | Sets Class 11 Maths Find Union and Intersection of Sets A, B, C and D If \[ A=\{1,2,3,4,5\},\ B=\{4,5,6,7,8\}, \] \[ C=\{7,8,9,10,11\},\ D=\{10,11,12,13,14\} \] Find: (i) \(A \cup B\) (ii) \(A \cup C\) (iii) \(B \cup C\) (iv) \(B \cup D\) (v) \(A

If A ⊂ B, Find A ∩ B and A ∪ B | Sets Class 11 Maths If A ⊂ B, Find A ∩ B and A ∪ B If \[ A \subset B \] then find: (i) \[ A \cap B \] (ii) \[ A \cup B \] Solution Since \[ A \subset B

Prove That X ⊆ Y for X = {8ⁿ − 7n − 1} and Y = {49(n − 1)} Prove That X ⊆ Y If \[ X=\{8^n-7n-1:n \in N\} \] and \[ Y=\{49(n-1):n \in N\} \] then prove that \[ X \subseteq Y \] Solution Let \[ x=8^n-7n-1 \] where \[ n \in N \]