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

For an n - variable Boolean function maximum number of prime implicants is

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