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negation
p and ~q
converse
if q then p
inverse
if ~p then ~q
contrapositive
if ~q then ~p
sufficient condition
if r then s
necessary condition
if not r then not s
modus ponens
if p then q
p
…q
modus tollens
if p then q
~q
…~p
prime
if n=rs, r or s = n
composite
n=rs, 1<r<n and 1<s<n
even
n=2k
odd
n=2k+1
rational
n=a/b, b=\=0
divisibility
n=dk, d=\=0
quotient remainder theorem
n=dq+r,