Answers: (i) We know that, A ∪ (A ∩ B) [A ∪ A = A] (A ∪ A) ∩ (A ∪ B) ∴ A ∩ (A ∪ B) = A (ii) A ∩ (A ∪ B) = A We know that, (A ∩ A) ∪ (A ∩ B) [A ∩ A = A] ∴ A ∪ (A ∩ B) =...
Answers: (i) Consider, A = {1, 2} B = {2, 3} C = {2, 4} A ∩ B = {2} A ∩ C = {2} Thus, A ∩ B = A ∩ C and B is not equal to C. (ii) A ⊂ B C–B ⊂ C–A Consider, x ∈ C– B x ∈ C and x ∉ B x ∈ C and x ∉ A...
Answers: (i) A ∪ B = B Proving, (iii)=(iv) Let us take, A ∪ B = B A ∩ B = A. A ⊂ B and A ∩ B = A Thus, (iii)=(iv) is proved. (ii) A ∩ B = A Proving, (iv)=(i) Let us take, A ∩ B = A A ⊂ B A ∩ B = A...
Answers: (i) A ⊂ B Proving, (i)=(ii) ( A ⊂ B) A–B = {x ∈ A: x ∉ B} All element of A is also an element of B ∴ A–B = ϕ Thus, (i)=(ii) Proved. (ii) A – B = ϕ Proving, (ii)=(iii) Let us take, A–B = ϕ...
Answer: A ⊂ B ⇒ A ∩ B = A Consider, p ∈ A ⊂ B x ∈ B Let, p ∈ A ∩ B x ∈ A and x ∈ B x ∈ A and x ∈ A ∴ (A ∩ B) = A
Answers: (i) Consider, p ∈ B p ∈ B ∪ A ∴ B ⊂ A ∪ B (ii) Consider, p ∈ A ∩ B p ∈ A and p ∈ B ∴ A ∩ B ⊂ A
Answers: (i) LHS, A ∪ B = {x: x ∈ A or x ∈ B} A ∪ B = {2, 3, 5, 7, 9} (A∪B)’ = Complement of (A∪B) with U. (A∪B)’ = U – (A∪B)’ U – (A∪B)’ = {x ∈ U: x ∉ (A∪B)’} U = {2, 3, 5, 7, 9} (A∪B)’ = {2, 3,...
Answers: (i) LHS, (B ∩ C) = {x: x ∈ B and x ∈ C} (B ∩ C) = {5, 6} A – (B ∩ C) = {x ∈ A: x ∉ (B ∩ C)} A = {1, 2, 4, 5} (B ∩ C) = {5, 6} (A – (B ∩ C)) = {1, 2, 4} RHS, A – B = {x ∈ A: x ∉ B} A = {1,...
Answers: (i) LHS, B–C = {x ∈ B: x ∉ C} B = {2, 3, 5, 6} C = {4, 5, 6, 7} B–C = {2, 3} (A ∩ (B – C)) = {x: x ∈ A and x ∈ (B – C)} (A ∩ (B – C)) = {2} RHS, (A ∩ B) = {x: x ∈ A and x ∈ B} (A ∩ B) =...
Answers: (i) LHS, (B ∩ C) = {x: x ∈ B and x ∈ C} (B ∩ C) = {5, 6} A ∪ (B ∩ C) = {x: x ∈ A or x ∈ (B ∩ C)} A ∪ (B ∩ C) = {1, 2, 4, 5, 6} RHS, (A ∪ B) = {x: x ∈ A or x ∈ B} (A ∪ B) = {1, 2, 4, 5, 6}....
Answer: A ∪ {1, 2} = {1, 2, 3, 5, 9} The smallest set of A, A = {1, 2, 3, 5, 9} – {1, 2} ∴ A = {3, 5, 9}
Solution: Let’s consider as the set of people in the committee who speak French as F, and the set of people in the committee who speak Spanish as S. $n\left( F \right)\text{ }=\text{ }50$ $n\left( S...
Solution: Let’s consider C as the set of people who like cricket, and the set of people who like tennis as T. $n(C~\cup ~T)\text{ }=\text{ }65$ $n\left( C \right)\text{ }=\text{ }40$ $n(C~\cap...
Solution: Let’s consider the set of people who like coffee as C, and the set of people who like tea as T. $n(C~\cup ~T)\text{ }=\text{ }70$ $n\left( C \right)\text{ }=\text{ }37$ $n\left( T...
Solution: It is known that $n\left( X \right)\text{ }=\text{ }40$ $n(X~\cup ~Y)\text{ }=\text{ }60$ $n(X~\cap ~Y)\text{ }=\text{ }10$ This can be written as $n(X~\cup ~Y)\text{ }=~n\left( X...
Solution: It is known that $n\left( S \right)\text{ }=\text{ }21$ $n\left( T \right)\text{ }=\text{ }32$ $n(S~\cap ~T)\text{ }=\text{ }11$ This can be written as $n~(S~\cup ~T)\text{ }=~n~\left( S...
Solution: Let’s consider the set of people who speak Hindi as H, and the set of people who speak English as E. It is known that $n(H~\cup ~E)\text{ }=\text{ }400$ $n\left( H \right)\text{ }=\text{...
Solution: Provided $n\text{ }\left( X\text{ }\cup \text{ }Y \right)\text{ }=\text{ }18$ $n\text{ }\left( X \right)\text{ }=\text{ }8$ $n\text{ }\left( Y \right)\text{ }=\text{ }15$ This can be...
Solution: Provided $n\text{ }\left( X \right)\text{ }=\text{ }17$ $n\text{ }\left( Y \right)\text{ }=\text{ }23$ $n\text{ }\left( X\text{ }\cup \text{ }Y \right)\text{ }=\text{ }38$ This can be...