1. Nov 15, 2006

### MathematicalPhysicist

how do i show that Y^(XU{x})=(Y^X)x(Y^{x}) where X and Y are finite sets, and {x} is a singleton.
obvisouly i need to show that one set is contained in another and vice versa, the problem is how to do so?

Last edited: Nov 15, 2006
2. Nov 18, 2006

### MathematicalPhysicist

for those who havent undersatand, i need to prove |Y^X|=|Y|^|X|
i tried to prove it in induction on the exponent but i got to what i posted in the first post in this thread, can someone help me on this here?

3. Nov 18, 2006

### matt grime

Just write down a bijection, in the first post. Though the result you want to prove in the second post follows from counting the elements directly.

4. Nov 18, 2006

### MathematicalPhysicist

you mean because the set of all functions from X to Y, its cardinal equals the number of possible mappings from X to Y, which is |Y|^|X|, right?
still i think that i need a rigorous proof for this, and counting isnt as rigouros.

5. Nov 18, 2006

### matt grime

Of course counting is rigorous.