Maharashtra Board Solutions for Chapter: Mathematical Logic, Exercise 2: Exercise 1.2

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

$\left[~\left(~p\wedge ~q\right)\right]\vee q$

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

$\left[\left(p\to q\right)\wedge q)\right]\to p$

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

$\left(p\leftrightarrow q\right)\wedge \left(p\to ~q\right)$

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

$~\left(~q\wedge p\right)\wedge q$

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

$\left(p\wedge ~q\right)\leftrightarrow \left(p\to q\right)$

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

$\left(~p\to q\right)\wedge \left(p\wedge r\right)$

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

$\left[p\to \left(~q\vee r\right)\right]\leftrightarrow ~\left[p\to \left(q\to r\right)\right]$

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

$\left[\left(p\to q\right)\wedge ~q\right]\to ~p$