Question

If ξ = { w } and A = { x | x ∈ w and x ≤ 10 } , then A' is​

Answer 1

Answer:

ξ={0,1,2,3,4,5,6,7,8,9,10}

A={5,6,7,8,9,10}

B={3,4,5,6,7}

(A∪B)

′

=A

′

∩B

′

First consider the Left hand side (LHS) =(A∪B)

′

(A∪B)={5,6,7,8,9,10}∪{3,4,5,6,7}

(A∪B)={3,4,5,6,7,8,9,10}

(A∪B)

′

=ξ−A∪B={0,1,2,3,4,5,6,7,8,9,10}−{3,4,5,6,7,8,9,10}

(A∪B)

′

={0,1,2}

Therefore, LHS (A∪B)

′

={0,1,2}

Then, Right hand side (RHS) =A

′

∩B

′

A

′

=ξ−A={0,1,2,3,4,5,6,7,8,9,10}−{5,6,7,8,9,10}

A

′

={0,1,2,3,4}

B

′

=ξ−B={0,1,2,3,4,5,6,7,8,9,10}−{3,4,5,6,7}

B

′

={0,1,2,8,9,10}

A

′

∩B

′

={0,1,2,3,4}∩{0,1,2,8,9,10}

A

′

∩B

′

={0,1,2}

Therefore, RHS A

′

∩B

′

={0,1,2}

By comparing LHS and RHS (A∪B)

′

=A

′

∩B

′