$(12\mathrm{.}5$ points$)$ Each of three coins has two sides, heads and tails. Represent the heads or tails status of each coin by a logical variable $($ A for the first coin, $B$ for the second coin, and $C$ for the third$)$ where the logical variable is $1$ for heads and $0$ for tails. The three coins are placed on a table in a straight line such that $B$ is adjacent to $A,$ and $C$ is adjacent to $B.$ There is no adjacency between A and $C.$ Write a logic function $F(A,B,C)$ which is $1$ iff no two adjacent coins have the same outcome after a toss of the coins. Express $F$

$($a$)$ as a minterm expansion $($Use $m-$notation$)$

$($b$)$ as a maxterm expansion $($Use $M-$notation$)$