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Prove that if there is a bijection between two sets A and B, then there is a bijection between P(A) and P(B).
I don't think I can use an example because this is a for all statement.
I am pretty stuck here.
Please someone help me!!!!
Let A be the set of subsets of [n] that havew even size, and let B be the set of subsets of [n] that have odd size. Establish a bijection from A to B, thereby proving that |A| = |B|. (Such a bijection is suggested below for n=3.)
A {empty set, {2,3}, {1,3}, {1,,2}}
B { {3} , {2} , {1} , {1,2,3}}
Someone out there please know what this stuff is.
I submitted a first draft to the teacher yesterday and he had a problem with me using "S" as an element of the set A, when S is just all of the elements of the set A. Tell me if you see any problems before I submit this assignment.
Yes, you got me off on the right start. I appreciate it.
Thank you very much.
I am lost on this proof.
Let A be a set such that If S is an element of A, then S is contained in A, and let P(A) be the power set of A. Prove that if S is an element of P(A), then S is contained in P(A).
P(A) is the power set of A.
Please someone know what this stuff is!!!!!!