Mathematical Re...

$$\sim \left[ p\wedge (\sim q) \right] =$$

If $$p, q, r$$ are simple proportions with truth values $$T, F, T$$, then the truth value of $$(\sim p\vee q)\wedge \sim r \Rightarrow p$$ is

$$p \leftrightarrow q$$ is equivalent to

The inverse of the propositions $$(p \wedge \sim q) \rightarrow r$$ is____.

If $$p$$ is $$T$$ and $$q$$ is $$F$$, then which of the following have the truth value $$T$$?
$$(i)p\vee q$$
$$(ii)\sim p\vee q$$
$$(iii)p\vee (\sim q)$$
$$(iv)p\wedge (\sim q)$$

If $$p:3$$ is a prime number and $$q:$$ one plus one is three, then the compound statement "It is not that $$3$$ is a prime number or it is not that one plus one is three" is

If $$p$$'s truth value is $$T$$ and $$q$$'s truth value is $$F$$, then which of the following have the truth value $$T$$?
(i) $$p\vee q$$
(ii) $$\sim p\vee q$$
(iii) $$p\vee (\sim q)$$
(iv) $$p\wedge (\sim q)$$

Which of the following is not a logical statement?

The truth values of $$p, q$$ and $$r$$ for which $$(p \wedge q) \vee (\sim r)$$ has truth value F are respectively

$$\left( p\wedge \sim q \right) \wedge \left( \sim p\wedge q \right) $$ is a :