Boolean algebra on Logic Circuit

Question

I need help with this function to create a truth table: F(a, b, c) = a'c' + abc + ac' Use Boolean laws and theorems to reduce the given function I need the reduced and original function truth table From there I will be able to create a logic gate circuit Thanks

Answer 1

Notice $F(a,b,c) = c'(a'+a) +abc.$ The term $a' + a$ will always be $1$. So we have $F(a,b,c) = c' + abc$. To find the truth table just input all different combinations of $a, b, c$ and write down the respective outputs.