Question

You have been provided with the following logic

Answer 1

If X and Y are Boolean variables, then X + Y represents disjunction (OR) and XY represents conjunction (AND), and X' denotes the negation (NOT). So X + Y = 1 if either X = 1 or Y = 1, and XY = 1 only if both X = 1 or Y = 1.

Now,

(X + Y) (X + Y') = XX + YX + XY' + YY'

… = X + X (Y + Y') + 0

… = X + X

… = X

or in table form,

$\begin{array}{c|cccc}X&1&1&0&0\\Y&1&0&1&0\\Y'&0&1&0&1\\X+Y&1&1&1&0\\X+Y'&1&1&0&1\\(X+Y)(X+Y')&1&1&0&0\end{array}$