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Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
A necessary and sufficient condition requires that both of the implications and (the latter of which can also be written as ) hold. The first implication suggests that S is a sufficient condition for N , while the second implication suggests that S is a necessary condition for N .
Tautological consequence can also be defined as ∧ ∧ ... ∧ → is a substitution instance of a tautology, with the same effect. [2]It follows from the definition that if a proposition p is a contradiction then p tautologically implies every proposition, because there is no truth valuation that causes p to be true and so the definition of tautological implication is trivially satisfied.
"In terms of implications, if implemented and prolonged, Canada and Mexico would likely go into an imminent recession and potentially see a bigger shock than Brexit was for the UK. It should ...
The hearer can now draw the contextual implications that +> Susan needs to be cheered up. +> Peter wants me to ring Susan and cheer her up. If Peter intended the hearer to come to these implications, they are implicated conclusions. Implicated premises and conclusions are the two types of implicatures in the relevance theoretical sense. [51]
The material conditional (also known as material implication) is an operation commonly used in logic.When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false.
Suppose we are given that .Then we have by the law of excluded middle [clarification needed] (i.e. either must be true, or must not be true).. Subsequently, since , can be replaced by in the statement, and thus it follows that (i.e. either must be true, or must not be true).
On today's episode of The College Football Enquirer, Dan Wetzel, Ross Dellenger and SI's Pat Forde discuss two underrated Big Ten matchups in Week 9. They unpack the headlines for Wisconsin vs ...