1. tautologies without truth table.

The question is : show that the following propositions are tautologies without using truth table.
(p∨~q)∧(~p∨~q)∨q

Can anyone help me? Is it correct what i am doing?

2. Re: tautologies without truth table.

Originally Posted by jayjdd2
The question is : show that the following propositions are tautologies without using truth table. (p∨~q)∧(~p∨~q)[COLOR=#242729][FONT=MathJax_Main]∨q
I find your notation confusing. Using a standard order of operation here is my take.
$\begin{gathered} \left\{ {(p \vee \neg q) \wedge (\neg p \vee \neg q)} \right\} \vee q &\equiv \left\{ {(p \wedge \neg p) \vee \neg q} \right\} \vee q \\ &\equiv \left\{ {(F) \vee \neg q} \right\} \vee q \\ &\equiv \left\{ {\neg q} \right\} \vee q \\ &\equiv T \\ \end{gathered}$

3. Re: tautologies without truth table.

Thanks! I understand it.