Using 2:1 Mux, (2 inputs, 1 output and a SELECT line)
a) NOT :Give the input at the select line and connect I0 to 1 & I1 to 0. So if A is 1, we will get I1 that is 0 at the O/P.
b) AND: Give input A at the select line and 0 to I0 and B to I1. O/p is A & B
c) OR: Give input A at the select line and 1 to I1 and B to I0. O/p will be A | B
d) NAND: AND + NOT implementations together
e) NOR: OR + NOT implementations together
f) XOR: A at the select line B at I0 and ~B at I1. ~B can be obtained from (a)
g) XNOR: A at the select line B at I1 and ~B at I0

Using 2:1 Mux, (2 inputs, 1 output and a select line)
a) NOT :Give the input at the select line and connect I0 to 1 & I1 to 0. So if A is 1, we will get I1 that is 0 at the O/P.
b) AND: Give input A at the select line and 0 to I0 and B to I1. O/p is A & B
c) OR: Give input A at the select line and 1 to I1 and B to I0. O/p will be A | B
d) NAND: AND + NOT implementations together
e) NOR: OR + NOT implementations together
f) XOR: A at the select line B at I0 and ~B at I1. ~B can be obtained from (a)
g) XNOR: A at the select line B at I1 and ~B at I0