Constructing a truth table?

Not sure how you're using the symbols, but for the sake of example I'll assume + means XOR and ' means NOT.

So, first you make columns for x and y and permute them across their combinations, like this:

X Y

T T

T F

F T

F F

Then, since you will need them later, columns for NOT X and NOT Y which just show the opposite of hte X and Y columns.

Then you make a column for X XOR Y and fill in the cell with the resultant value according to the original values in the X and Y columns .

Then a column for X AND Y, similarly computed.

Then a Column for NOT(X XOR Y) computed from negating the X XOR Y column.

Next, a column for (NOT X) AND (NOT Y)

and then finally a column for the entire equality statement derived from where NOT(X XOR Y) has the same value as (NOT X) AND (NOT Y). Done.

AND? you can't?

example: if x and y are both ZERO. Then on the left side you get the inverted value of (0 ored with 0) = 1. On the right side you have inverted x ANDED with inverted Y which will give you 1 ANDED with 1 = 1. So both sides are same hence equation is correct.

Sounds like you need some wood.