Write down in words $\neg p$.

Write down in symbolic form the compound statement

$r:$ If $x$ is a multiple of $12$, then $x$ is a multiple of $6$.

Consider the compound statement

$s:$ If $x$ is a multiple of $6$, then $x$ is a multiple of $12$.

Identify whether $s:$ is the inverse, the converse or the contrapositive of $r$.

Consider the compound statement

$s:$ If $x$ is a multiple of $6$, then $x$ is a multiple of $12$.

Determine the validity of $s$. Justify your decision.

$x$ is not a multiple of $12$     (A1)     (C1)

$p \Rightarrow q$     (A1)(A1)(C2)

Note: Award (A1) for $\Rightarrow$, (A1) for $p$ and $q$ in the correct order.

Accept $q \Leftarrow p$.

Converse     (A1) (C1)

not valid     (A1)

for example $18$ is a multiple of $6$ and not a multiple of $12$     (R1)     (C2)

Notes: Do not award (A1)(R0). Any multiple of 6 that is not a multiple of $12$ can be accepted as a counterexample.