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 \[ n \in N \]

Find the Universal Set for Right Triangles and Isosceles Triangles Find the Universal Set for Right Triangles and Isosceles Triangles What universal set(s) would you propose for each of the following: (i) The set of right triangles. (ii) The set of isosceles triangles. Solution (i) A suitable universal set for the set of right triangles

How Many Elements Has P(A), if A = Φ? | Sets Class 11 Maths How Many Elements Has P(A), if A = Φ? How many elements has \[ P(A) \] if \[ A=\Phi \] ? Solution Since \[ A=\Phi \] there are \[ 0 \] elements in \[ A \] Number of elements in \[