$1.$ Explain the following Logic gates with a neat diagram and $3-$variable truth table $(8$ marks$)$

a$.$ NAND gate

b$.$ XOR gate

$2.$ Draw the circuit for the given Boolean Expression. $(8$ marks$)$

a$.$ X$=($A$+$B$)($C$+$D$)$

b$.$ X$=$AB$+$CD

$3.$ Simplify the following Boolean Expression using Boolean Identities. $(4$ marks$)$

F$=$ A$$B$$C $+$ A$$BC $+$ AB$$