Question

For any three sets P,Q and R,P-(Q∩R)is

A)P-(Q∪R) B)(P∩Q)-R C)(P-Q)∪(P-R) D)(P-Q)∩(P-R)​

Answer 1

P - (Q ∩ R) = (P - Q) ∪ (P - R)

Given :

Three sets P , Q , R

To find :

P - (Q ∩ R) is

A) P - (Q ∪ R)

B) (P ∩ Q) - R

C) (P - Q) ∪ (P - R)

D) (P - Q) ∩ (P - R)

Solution :

Step 1 of 2 :

Write down the given set

Here the given set is P - (Q ∩ R)

Step 2 of 2 :

Choose the correct option

P - (Q ∩ R)

= P ∩ (Q ∩ R)' [ By De Morgan's Law ]

= P ∩ ( Q' ∪ R' )

= ( P ∩ Q' ) ∪ ( P ∩ R' ) [ By Distributive Law ]

= (P - Q) ∪ (P - R)

Hence the correct option is C) (P - Q) ∪ (P - R)

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