202110211114 LGT

$\stackrel{\text{sufficient}}{\overbrace{P}}\to \stackrel{\text{necessary}}{\overbrace{Q}}$

Provided that $P\to Q$:

• $P$ implies $Q$ if $P$, then $Q$ $Q$ if $P$ $P$ only if $Q$ $Q$ when $P$ $Q$ whenever $P$ $Q$ follows from $P$
• A necessary condition for $P$ is $Q$. $Q$ is necessary for $P$
• A sufficient condition for $Q$ is $P$. $P$ is sufficient for $Q$
• $Q$ unless $\neg P$