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# Use the truth table to establish which of the following statements are tautologies and which are contradictions.

(iii)$(p\wedge (\sim q)) \vee ((\sim p)\vee q)$.

This question is the third part of multipart q1

Can you answer this question?

## 1 Answer

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Toolbox:
• If $p$ and $q$ are two simple statements $p\wedge$ is the conjunction of $p$ and $q$ and $p \vee q$ is the disjunction .Negation of a statement $p$ is denoted by $\sim p$
• Rules for conjunction :
• $A_1$: The statement $p\wedge q$ has the truth table value $T$ whenever both $p$ and $q$ have the truth value $T$
• $A_2$: The statement $p\wedge q$ has the truth value $F$ whenever either $p$ or $q$ or both have the truth value $F$
• $A_3$: The statement $p\vee q$ has the truth value $F$ whenever both $p$ and $q$ have the truth value $F$.
• $A_4$: The statement $p\vee q$ has the truth value $T$ whenever either $p$ or $q$ or both have the truth value $T$
• A statement is tautology if the last column in the truth table is $T$ entirely.It is a contradiction if the last column is $F$ entirely.
The statement is a tautology
answered Sep 13, 2013

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