Question

Let B be a subset of a set A and let P(A:B)={X€P(A):X is superset of B}
(i) Show that:P(A:phi)=P(A)

Answer 1

Given: B is subset of a set A and let P (A:B) = { X € P(A) : X is superset of B}

To find: Show that:P(A: ∅ ) = P(A)

Solution:

• Now we have provided with B is subset of a set A.

                  P (A:B) = { X € P(A) : X is superset of B}

• Now we can write it as:

                  P (A:B) = { X € P(A) : B is a subset of X }

• So:

                  P (A:B) = { Set of all subsets of A which contains B in it }

• Now, we have:

                  P(A: ∅) = Set of all those subsets of A which contain ϕ in it.

                  P(A: ∅) = Set of all subsets of A = P(A)

Answer:

              So from solution we proved that P(A: ∅) = P(A)