if p, then q

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if _, then _

if p, then q

q if p

if p, then q

q provided that p

if p, then q

_ is a sufficient condition for _

p is a sufficient condition for q

_ only if _

p only if q

_ if _

q if p

_ is a necessary condition for _

q is a necessary condition for p

p implies q

q is a necessary condition for p

q ___ p

q is a necessary condition for p; q provided that p; q if p

_ provided that _

q provided that p

p only if q

q provided that p

q if p

q provided that p

p is a sufficient condition for q

q whenever p


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