Boolean expression correct or not?

Question

A teacher says the following is true:

XY + ¯X ¯Y = 1

Do you agree or not, if yes then why?
I don't because:
Z + ¯Z = 1 BUT if Z=XY then ¯Z is not equal to ¯X¯Y
in fact ¯Z = ¯(XY) = ¯X + ¯Y

any other opinions?

when I use ¯X, I do not mean negative X but X with an overbar hence ¯X is the complement of X

So first answer does not make sense.

The expression is:
X*Y + (complement of)X*(complement of)Y = 1

Answer 1

I don't agree with the teacher. It should be XY+(XY)'=1.

Answer 2

Keep in mind this is not multiplication and addition. XY is X and Y. What looks like minus signs should be over the X and Y and means "not". If you draw this as logic with contacts you will have X in series with Y, that is the XY or X and Y. You will then have notX is series with notY paralleled. The X and Y are like normally open contacts where as the not's are like normally closed contacts. If power can pass you have a 1.
In the equation you have: X and Y or notX and notY the result is 1.

Answer 3

It's true because the x +-x = 1 and y+ -y = 1 so 1*1 =1