The Boolean expression (X+Y)(X+$$\overline Y $$)+($$\overline {(X\overline Y ) + \overline X } $$ simplifies to

In the sum of products function f (x,y,z) = $$\sum {} $$m (2,3,4,5), the prime implicants are

The Boolean function Y=AB+CD is to be realized using only 2-input NAND gates. The minimum number of gates required is

The number of product terms in the minimized sum-of-product expression obtained through the following k-map is ( where , "d" denotes don't care states)