Tag: proofs in mathematics

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

$(p\wedge ∼q)\wedge ∼p$

$(p\wedge ∼q)\vee  ∼p$

$(p\wedge ∼q)\vee ∼p$

none of these

If I do not have a Siberian Husky, then I do not have a dog.

If I have a dog, then I have a Siberian Husky.

If I do not have a dog, then I do not have a Siberian Husky.

If I do not have a Siberian Husky, then I have a dog.

$(p\vee q)$

$[p\wedge(q)]$

$p\wedge(q)$

$p\vee(q)$

a tautology

a contradiction

neither a tautology nor a contradiction

cannot come to any conclusion