Given the Boolean functions F$1$ and F$2,$ show that

$($a$)$ The Boolean function E $=$ F$1+$ F$2$ contains the sum of the minterms of F$1$ and F$2.$

$($b$)$ The Boolean function G $=$ F$1$F$2$ contains only the minterms that are common to F$1$

and F$2$