Look at the truth table of AND gate. When any of the one input is zero output is always zero (or same as that input); when the other input is one, output is dependent on the other input and is same as the other input. Using this property we can draw AND gate in four different ways using 2:1 MUX as shown in the above figure.
Similar concept can be applied to create all basic gates from 2:1 MUX. I will publish all these in coming blog posts along with the elaborated