Tag: implications

$\left(p \rightarrow q\right)\leftrightarrow \left( \sim q \rightarrow \sim p \right) $

$\left[ \left( p\rightarrow q \right) \wedge \left( q\rightarrow r \right) \right]\rightarrow \left( p\rightarrow r \right) $

$\left( \sim p\vee q \right) \leftrightarrow \left( p\wedge \sim q \right) $

$p \rightarrow \sim p$

$p \vee ( q \wedge r )$

$( p \wedge q ) \wedge r$

$( p \vee q ) \vee r$

$p \rightarrow ( q \wedge r )$

$p \text { is true and } q \text{ is true}$

$p \text { is false and } q  \text{ is true}$

$p \text { is true and } q \text{ is false}$

both $p$ and $q$ are false

Mathematics is interesting implies that Mathematics is difficult

Mathematics is interesting implies and is implied by Mathematics is difficult

Mathematics is interesting and Mathematics is difficult

Mathematics is interesting or Mathematics is difficult

$p\vee \left( \sim q \right) \vee \sim p$

$\left( p\vee \sim q \right) \vee \sim p$

$p\wedge \sim \left( q\vee \sim p \right) $

none of these

$p \rightarrow \sim q$

$q \rightarrow \sim p$

$q \rightarrow p$

$\sim p \rightarrow \sim q$

$\sim q \rightarrow \sim p$

$(a)False$ and $(b)$ False

$(a)True$ and $(b)$ False

$(a)False$ and $(b)$ True

$(a)True$ and $(b)$ True

p$\rightarrow$q and $F$

q$\rightarrow$p and $T$

q$\rightarrow$p and $F$

p$\rightarrow$q and $T$

DeMorgan's Law

Conditional Law

Involution Law

Complement Law

$\sim P\vee Q$

$\sim P\wedge Q$

$\sim Q\wedge P$

$\sim Q\vee P$