Q8
From suitable properties of union and intersection deduce the following results

(i) A∩(AUB)=AU(A∩B)

SOLUTION:

Using the property of distributivity of intersection over union.

A∩(AUB)=(A∩A)U(A∩B)=AU(A∩B)                                                                [∴A∩A=A]

(ii) AU(A∩B)=A∩(AUB)

SOLUTION:

By using the property of distributivity of union over intersection

AU(A∩B)=(AUA)∩(AUB)=A∩(AUB)                                                                 [∴A∩A=A]