BITSAT2017MathematicsSets and RelationsActual
Let A and B be two sets such that A ∩ X = B ∩ X = ϕ and A ∪ X = B ∪ X for same set X . Then,
Options
- AA = B
- BA = X
- CB = X
- DA ∪ B = X
Correct answer
A. A = B
Step-by-step solution
Given, that, A ∪ X = B ∪ X ⇒ A ∩ ( A ∪ X ) = A ∩ ( B ∪ X ) ⇒ ( A ∩ A ) ∪ ( A ∩ X ) = ( A ∩ B ) ∪ ( A ∩ X ) [Using distributive law] ⇒ A ∪ ϕ = ( A ∩ B ) ∪ ϕ   [ ∵ A ∩ X = ϕ ] ⇒   A = A ∩ B . . . ( i ) Again, consider A ∪ X = B ∪ X ⇒ B ∩ ( A ∪ X ) = B ∩ ( B ∪ X ) ⇒ ( B ∩ A ) ∪ ( B ∩ X ) = ( B ͪ