Question

Q. Construct the truth tables for (p & q here are not above statement)

a) p V ~q
b) ~p V ~q
c) q -->p
d) ~(p-->q)-->r

Answer 1

$\begin{matrix} P & q&\tilde q &pv\tilde q\\ T&T&F&T\\ T&F&T&T\\ F&T&F&F\\ F&F&T&T\\ \end{matrix}\\ \begin{matrix} P & \tilde p& q&\tilde q &\tilde pv\tilde q\\ T&F&T&F&F\\ T&F&F&T&T\\ F&T&T&F&T\\ F&T&F&T&T\\ \end{matrix}\\ \begin{matrix} P & q&q\implies p\\ T&T&T\\ T&F&T\\ F&T&F\\ F&F&T\\ \end{matrix}\\ \begin{matrix} P & q&r&p\implies q&\tilde( p \implies q)&\tilde(p\implies q)\implies r\\ T&T&T&T&F&T\\ T&T&F&T&F&T\\ T&F&T&F&T&T\\ T&F&F&F&T&F\\ F&T&T&T&F&T\\ F&T&F&T&F&T\\ F&F&T&T&F&T\\ F&F&F&T&F&T\\ \end{matrix}\\$