contestada

in the statement "if it is cold,then i wear a jacket" is assumed to be true,is its converse,"if i wear a jacket,then is must be cold," also always true?

Respuesta :

konrad509

[tex] p [/tex] - it is cold

[tex] q [/tex] - I wear a jacket


[tex] p\Rightarrow q=1 [/tex]

therefore, the following are possible values of [tex] p [/tex] and [tex] q [/tex]

[tex] p=0 \wedge q=0\\p=0 \wedge q=1\\p=1 \wedge q=1 [/tex]

Now, if [tex] q\Rightarrow p [/tex] then we have

[tex] 0\Rightarrow 0=1\\1\Rightarrow 0=0 [/tex]

The second statement is false, so the statement from the question is NOT always true.



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