Using truth table, given any two Boolean functions F$1$ and F$2,$ prove that:

a$)$The Boolean function E $=$ F$1+$ F$2$ contains the sum of the minterms of F$1$ and F$2$ to be in the sum of products canonical form.

b$)$The Boolean function G $=$ F$1$F$2$ contains only the minterms common to F$1$ and F$2.$