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If A is a necessary condition for B, then the logical relation between them is expressed as "If B then A" or "B only if A" or "B → A" (B implies A).
If A is a sufficient condition for B, then the logical relation between them is expressed as "If A then B" or "A only if B" or "A → B".
(from wikipedia)
If A is a sufficient condition for B, then the logical relation between them is expressed as "If A then B" or "A only if B" or "A → B".
(from wikipedia)
A necessary condition for a property P to hold is any condition which holds whenever P does. So if we're thinking of natural numbers (0,1,2,...) and P is 'x is a multiple of 4' then 'x is even' is a necessary condition as x can't be a multiple of 4 if it's not even (but it could still be even if it's not a multiple of 4)
A sufficient condition for a property P to hold is any condition which forces P to hold. So if this time we take P to be 'x is even' then 'x is a multiple of 4' would be a sufficient condition. Whenever x is a multiple of 4, it must be the case that x is even.
If a condition Q is both necessary and sufficient for a property P then P and Q are equivalent properties. That is P holds if and only if Q holds. e.g P is 'x is even' and Q is 'x=2y for some whole number y'
A sufficient condition for a property P to hold is any condition which forces P to hold. So if this time we take P to be 'x is even' then 'x is a multiple of 4' would be a sufficient condition. Whenever x is a multiple of 4, it must be the case that x is even.
If a condition Q is both necessary and sufficient for a property P then P and Q are equivalent properties. That is P holds if and only if Q holds. e.g P is 'x is even' and Q is 'x=2y for some whole number y'
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