Given $($please for all questions provide all the steps$)F^{\text{'}}(A,B,C,D)=m(0,3,5,6,8,11,12),$ find the minterm expansion for $F.$

Each of the 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. Write a logic function $F(A,B,C)$ which is $1$ if exactly one of the coins is heads after a toss of the coins.

a$)$ Write the truth table for $F.$

b$)$ Express $F$ as a minterm expansion.