Question

If A and B are two given sets then An(An B)' is equal to ​

Answer 1

Answer:

A∩(A∩B)

c

=A∩(A

c

∪B

c

) (De Morgan's Law)

=(A∩A

c

)∪(A∩B

c

)

=ϕ∪(A∩ϕB

c

)

∴A∩(A∩B)

c

=A∩B

c

Answer 2

Answer:

A∩(A∩B)

c

=A∩(A

c

∪B

c

) (De Morgan's Law)

=(A∩A

c

)∪(A∩B

c

)

=ϕ∪(A∩ϕB

c

)

∴A∩(A∩B)

c

=A∩B

c