From symbols to words and truth values

Statement

Let $p$ = ”$16$ is a perfect square”, $q$ = “green is a primary color”, $r$ = “the whale is a fish”. Here $p$ is true, while $q$ and $r$ are false. Rewrite each statement in words and give its truth value.

(i) $p \land q$ (ii) $\lnot r$ (iii) $p \to r$ (iv) $q \leftrightarrow r$ (v) $\lnot p \lor q$ (vi) $\lnot(p \land q)$

Solution

(i) ”$16$ is a perfect square and green is a primary color”: $T \land F = F$. (ii) “the whale is not a fish”: $\lnot F = T$. (iii) “if $16$ is a perfect square then the whale is a fish”: $T \to F = F$. (iv) “green is a primary color if and only if the whale is a fish”: $F \leftrightarrow F = T$. (v) ”$16$ is not a perfect square or green is a primary color”: $F \lor F = F$. (vi) “it is not the case that $16$ is a perfect square and green is primary”: $\lnot(T\land F)=\lnot F = T$.