Answer
a) $ c$, $ p$
b) true.
c) true.
Work Step by Step
a) Use the Identity, Idempotent, and Negation laws, we have:
$p\oplus p=(p\vee p)\wedge \sim (p\wedge p)=
(p)\wedge \sim (p)\equiv c$
$(p\oplus p)\oplus p=c\oplus p
=(c\vee p)\wedge \sim (c\wedge p)
=(p)\wedge \sim (c)=p\wedge t\equiv p$
b) Use the given table in this exercise, we can construct a truth table as shown with the top table, and we can conclude that the statement is true.
c) Use the above results, we can construct another truth table as shown with the bottom table. We can conclude that the statement is true.
