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# Mind Your Ps and Qs

##### Age 16 to 18 Short Challenge Level:

To do this question you need to be really sure what the two symbols $\Rightarrow$ and $\Leftrightarrow$ mean.

$p\Rightarrow q$ essentially means that IF $p$ is True THEN $q$ is true.

$p\Leftrightarrow q$ means that $p$ is true if and only if $q$ is true. Alternatively, they are either both true or both false.

To get started, pick one of the simpler looking statements for $p$.

Go through the other statements in turn and see which of them work as $q$ in $p\Rightarrow q$. You will soon be able to pair-off possible partners.

Finally, don't forget to read the details of the question carefully!