What is the equivalent to Y AND (X AND Y)

I will give a hint about how to easily simplify the expression. The AND operation is commutative and associative, meaning that it does not matter what order the terms are in or what order the AND operations are applied. Let me know if you need further help.

Is this a homework problem? If so, I don’t want to respond with a full answer/explanation if not I (or someone else) can post an explanation.

By any argument Y and (Y and X) is equivalent to Y and X
It’s tautologous. ....just think about it for a minute…you’ll get the gist of it.

Y and (Y and X) can be split across the two. So that becomes (Y and Y) and (Y and X).
Since (Y and Y) is just plain silly we can consider that redundant.
So Y and X is left.

@LeotCol: I think your explanation is incorrect. ”(Y and Y)” becomes “Y” (not nothing), and we’re back at “Y and (Y and X)”

Consider the truth table to see that they are equivalent:
Y={0,1}
Y | Y and Y
1 | 1
0 | 0

Perhaps you meant: “Y and (Y and X)” = ”(Y and Y) and X” = “Y and X”.

It’s Y AND X, because Y is necessarily true for either statement to be true, so it’s redundant.

Oh well…

Y AND (X AND Y) = Y AND (Y AND X) = (Y AND Y) AND X = Y AND X

This is a good example of how much better we are at informal logic than formal logic. If I said that I have to mail a letter and I also have cut the grass and mail a letter, you would probably suspect there is something wrong with me, since it is obvious that I could have just said that I have to cut the grass and mail a letter. You could use this intuition to provide another way of showing the statement is equivalent to Y AND X.

The statement is true if and only if Y is true and both X and Y are true. But if both X and Y are true then it must be the case that Y is true, so the first part is redundant and we are left with just Y AND X.
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@LostInParadise Thats true. Formal logic is much more useful in complex situations than simple ones.