Question

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?

Answer 1

`p` - it is cold

`q` - I wear a jacket

`p\Rightarrow q=1`

therefore, the following are possible values of
`p` and
`q`

`p=0 \wedge q=0\\p=0 \wedge q=1\\p=1 \wedge q=1`

Now, if
`q\Rightarrow p` then we have

`0\Rightarrow 0=1\\1\Rightarrow 0=0`

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