Question

U={a,b,c,d,e,f,g,h},p={a,d,f}.verify(P')'=p​

Answer 1

Three sets A,B and C are said to be associative if A∩(B∩C)=(A∩B)∩C.

Here, the given sets are P={a,b,c,d,e}, Q={a,e,i,o,u} and C={a,c,e,g}

Let us first find P∩(Q∩R) as follows:

P∩(Q∩R)={a,b,c,d,e}∩({a,e,i,o,u}∩{a,c,e,g})={a,b,c,d,e}∩{a,e}={a,e}........(1)

Now we find (P∩Q)∩R as follows:

(P∩Q)∩R=({a,b,c,d,e}∩{a,e,i,o,u})∩{a,c,e,g}={a,e}∪{a,c,e,g}={a,e}........(2)

Since equation 1 is equal to equation 2, therefore, P∩(Q∩R)=(P∩Q)∩R

Hence, the sets P,Q and R satisfies the associative property of intersection..