Question

For any sets A and B show that
i) (A∩B)∪(A-B)=A

ii) A∪(B-A)=A∪B
Please solve this step by step

Answer 1

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Step-by-step explanation:

ANSWER ::

Proof of (A∩B)∪(A-B)=A ::

(A∩B)∪(A-B)

= ( A ∩ B ) ∪ ( A ∩ B' )

= A∩ ( B ∪ B')

= A ∩ U

= A

Proof of A∪(B-A)=A∪B ::

A∪(B-A)

= A∪ (B ∩ A' )

= ( A∪B ) ∩ ( A∪ A')

=( A∪B ) ∩ U

= ( A∪B )

Where U = Universal Set