Question

Let U= {2,4,6,8,10,12,14,16}
A={2,4,6,8)
B={10,12,14,16), then verify that
(1) (A)' = A
(ii) A and A' =Q
(iii)(B') '=B​

Answer 1

1. A'= U - A

A'= { 2,4,6,8,10,12,14,16 } - { 2,4,6,8,}

A'= { 10,12,14,16}

A'= B

(A') ' = U - A'

(A') ' = {2,4,6,8,10,12,14,16} - {10, 12,14,16}

(A') ' = { 2,4,6,8}

(A') ' = A

2. In chapter SETS *And means UNION*

A U A' = {2, 4,6,8,10,12,14,16}

A U A' = Rational number

A U A' = Q

3. B' = U - B

B' = { 2,4,6,8,10,12,14,16} - {10,12,14,16}

B' = {2,4,6,8 }

B' = A

(B') ' = U - B'

(B') ' = { 2,4,6,8,10,12,14,16} - {2,4,6,8 }

(B') ' = { 10,12,14,16}

(B') ' = B