Tag: mathematical logic

Which of the following proposition is a contradiction?

Which of the following is not true (where $p, q$ and $r$ take truth values and $t$ is a tautology, $c$ is a contradiction)

$p,q,r$ are $3$ statement such that $(p\rightarrow q)\wedge (q\rightarrow r)\Rightarrow (p\rightarrow r)$ is 

The statement $[p \wedge (p \rightarrow q)]\rightarrow q$,is :

$p,q,r$ are $3$ statement such that $(p \rightarrow q)\wedge (q \rightarrow r)\Rightarrow (P \rightarrow r)$ is

Which of the following is a tautology?

The proposition $p\vee (\sim p\vee q)$ is a 

The only statement among the followings that is a tautology is

The simplifed form of $(p \vee q)\vee (\sim p \wedge q)$ is

$p,q,r$ are $3$ statements such that $\left(p\rightarrow q\right)\wedge \left(q\rightarrow r\right)=Rightarrow \left(p\rightarrow r\right)$ is