Let A be a set and consider the statement x PA x A The next

Let A be a set, and consider the statement ({x} P(A)) (x A) The next paragraph claims to prove this statement. Is this proof correct? Explain why or why not. Suppose x is an element of A. Then, by definition of the power set, there will be a singleton set containing x in P(A), that is, {x} P(A). Therefore, {x} P(A) x A.

Solution

Yes it is true

x is an element of A. Then, by definition of the power set, there will be a singleton set containing x in P(A), that is, {x} P(A). Therefore, {x} P(A) x A.

Power set contains all possibilities of having set of A

That is null set, single ton set ,..... And the given set itself.

Hence if element is in A then it\'s single ton set is in power set