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The Question:

Let X be a set with n elements, say S = {s

_{1}, s

_{2},..., s

_{n}}

Let B be the set of binary numbers with n digits. That is, sequences of n terms, each

of which is 0 or 1.

Define f : P(S) --> B (power set of S) as follows: the image of X ∈ P(S) is the

binary sequence b

_{1}b

_{2}....b

_{n}where b

_{i}is the truth value of the statement b

_{i}∈ X, for

i = 1, 2, ..., n.

Prove that f is a 1-1 correspondence.

My Work so far:

If A

_{1}= A

_{2}= A

_{n}, there are n-try relation and A is a subset of A

^{n}= A x A x ... x A = {(a

_{1,}, a

_{2}, ..., a

_{n}) ia

_{i}+ A for each i = 1, ...,n}

Prove: that there are n-tuples.

I am not sure where to go from here, or if my work is heading in the right direction

Any help would be much appreciated!