Reciprocal

See also: Reciprocal (homonymy)

The reciprocal is a relation of Implication.

If there are two proposals has and B, here both implications which one can form using these proposals:

$A\; \backslash Rightarrow\; B$

$B\; \backslash Rightarrow\; A$

These implications are reciprocal one of the other: the first is the reciprocal second and the second is the reciprocal first.

If the first implication is considered, is a sufficient condition of B has whereas if one considers the second, has is a requirement of B.

When an implication and its reciprocal are checked, there is then equivalence:

$(has\; \backslash \; Rightarrow\; B)\; \backslash \; and\; (B\; \backslash \; Rightarrow\; A)\; \backslash \; Rightarrow\; (has\; \backslash \; Leftrightarrow\; B)$

Example of implication and reciprocal in the current language:

If the following proposals are considered: “ There is fire ” and “ There is smoke ” then:

The implication “ If there is fire, there is smoke ” has for reciprocal “ If there is smoke, there is fire ”

Attention with distinguishing well contraposée and reciprocal.

reciprocal

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