# Discrete maths

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• Mar 3rd 2009, 11:42 AM
sabina_19
Discrete maths
this question is confusing i dont understand it
• Mar 3rd 2009, 01:20 PM
Soroban
Hello, sabina_19!

It seems clear enough . . . What part is confusing?

Quote:

By using the appropriate truth tables, decide whethr
each of the following is tautology, absurdity, or contingency.

A tautology is always true.
An absurdity is always false.
A contingency is sometime true, sometimes false. .("It depends.")

$\displaystyle (a)\;\;\begin{array}{|c||ccc|}\hline p & p & \to & p \\ \hline \hline T & T & {\color{blue}T} & T \\ \hline F & F & {\color{blue}T} & F \\ \hline \end{array}\qquad \text{Tautology}$

$\displaystyle (b)\;\;\begin{array}{|c||ccc|}\hline p & p & \to & \sim\!p \\ \hline \hline T & T & {\color{blue}F} & F \\ F & F &{\color{blue}T} & T \\ \hline \end{array}\qquad\text{Contingency}$

$\displaystyle (c)\;\;\begin{array}{|c||ccc|} \hline p & p & \wedge & \sim\!p \\ \hline \hline T & T& {\color{blue}F} & F \\ \hline F & F & {\color{blue}F} & T \\ \hline \end{array}\qquad\text{Absurdity}$