Tag: principle of mathematical induction

$ p\Rightarrow q$

$ (\sim p)\Rightarrow (\sim q)$

$ (\sim q)\Rightarrow (\sim p)$

$ (\sim q)\Rightarrow p$

$p$

$\sim p$

$\sim q$

$q$

All slow learners attend this school.

All slow learners do not attend this school.

Some slow learners attend this school.

Some slow learners do not attend this school.

No slow learners do not attend this school.

$p\vee (\sim  q\wedge r)$

$p\vee q\wedge r$

$p\vee (\sim  q\wedge \sim r)$

$\sim p\vee (\sim q\wedge r)$

tautology.

contradiction.

neither a tautology nor a contradiction.

tautology and contradiction.

$\dfrac {1}{2}$ is rational or $\sqrt {3}$ is irrational

$\dfrac {1}{2}$ is not rational or $\sqrt {3}$ is not irrational

$\dfrac {1}{2}$ is not rational or $\sqrt {3}$ is irrational

$\dfrac {1}{2}$ is rational and $\sqrt {3}$ is irrational

$\sim q\Rightarrow p$

$p\Rightarrow q$

$\sim p\vee q$

$p\Leftrightarrow q$

$p \leftrightarrow q$

$p \rightarrow q$

$p \leftarrow q$

$p \vee q$

$p \vee q$

$p \rightarrow q$

$p \leftarrow q$

None of these

F, T, F

F, F, F

T, T, T

T, F, F