Class 11

Math

JEE Main Questions

Sets

Using properties of sets, show that(i) $A∪(A∩B)=A$ (ii) $A∩(A∪B)=A$.

**Solution: **Solution: (i) $A∪(A∩B)$

$=(A∪A)∩(A∪B)$ by distributive property

$=A∩(A∪B)$

$=A$ =RHS, hence proved

(ii) $A∩(A∪B)=A$

$=(A∩A)∪(A∩B)$ by distributive property

$=A∪(A∩B)$

$=A$= RHS, hence proved