Prove: Let S and T be sets. If there exists and injection from |S| --> |T| then there exists an injection from |P(S)|-->|P(T)|

(P(S) and P(T) represent the power sets of each)

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- Sep 22nd 2008, 08:47 AMGoldendoodleMomPower Sets
Prove: Let S and T be sets. If there exists and injection from |S| --> |T| then there exists an injection from |P(S)|-->|P(T)|

(P(S) and P(T) represent the power sets of each) - Sep 22nd 2008, 09:15 AMPlato
Here is a bit of notation.

That is called the image set of under .

Now it is clear that we have , so we must prove that if

Of course to do that you must show . - Sep 22nd 2008, 09:35 AMGoldendoodleMomPower Sets
The proof is regarding the cardinality of the sets and power sets. Does that change the strategy?

- Sep 22nd 2008, 09:43 AMPlato