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Which one of the following operations on...

Which one of the following operations on sets is not correct where B' denotes the complement of B?

A

`(B'-A')uu(A'-B')=(AuuB)-(AnnB)`

B

`(A-B)uu(B-A)=(A'uuB')-(A'nnB')`

C

`(B'-A')nn(A'-B')=(B-A)nn(A-B)`

D

`(B'-A')nn(A'-B')=(B-A')uu(A'-B)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let there be two sets A and B and universal set of A and B, be U.
Then drawing these sets on a Venn-diagram, four regions are created as shown in the figure :

B `-=` regions b, c
B' `-=` regions a, d
`A -=` regions a, b
`A' -=` regions c, d
A-B `-=` region a
B-A `-=` region c
B'-A' `-=` region a
A'-B' `-=` region c
B-A' `-=` region b
A'-B `-=` region d
From these we check the operations given in the choice. choices (a), (b) and (c ) are correct
(d) LHS = region `annc=phi`
RHS = region `b uu` region d = b, d.
So, for (d) LHS `ne` RHS
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