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

(iv)$q\vee (p\vee(\sim q))$. This question is the fourth part of multipart q1

1 Answer

  • 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 :
  • $A_3$: 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
$\begin{matrix} p & q & \sim q & p \vee (\sim q) &q\vee (p\vee(\sim q)) \\ T&T & F& T &T \\ T & F & T &T &T \\ F& T & F & F &T \\ F& F & T & T & T \end{matrix}$
answered Sep 13, 2013 by sreemathi.v
edited Mar 20, 2014 by balaji.thirumalai