How Does Inverting Inputs Affect a 3-Input XOR Gate?

[hime]

Homework Statement

An Xor gate has 3 inputs w x y and its output is z. If you invert one of the inputs, what will the output be? Show this in terms of a boolean expression and no matter which input you invert, the output will be the same.

What is this type of gate called?
Also, what happens if you invert all three inputs?

Homework Equations

w XOR x XOR y = z
w'x'y + w'xy' + w'xy + wx'y' + wx'y + wxy' = z => expanding xor using and or and not gates

The Attempt at a Solution

If you invert one of the inputs then still you will have 2 combinations of w,x,y for which z=0 and the rest of the input combinations =1. But I do not see how to find the new output function z when you invert one of the input and then find a special gate for that expression. Just out of guessing, I think the gate is XNOR because it is a special gate often used in boolean expressions. Also, if all the inputs are inverted then it would still be an xor right?

 

[eumyang]

w'x'y + w'xy' + w'xy + wx'y' + wx'y + wxy' = z => expanding xor using and or and not gates

You sure about that? I thought it would be this:
w'x'y + w'xy' + wx'y' + wxy = z
for XOR.

Also, if all the inputs are inverted then it would still be an xor right?

No, it wouldn't.