Discrete Logic Determine whether the following argument is v

Discrete Logic:

Determine whether the following argument is valid. If valid, explain how you decided (rules/equivalences/etc). If not valid, explain why not.

i)   If I drive to work, then I will arrive tired.

ii) I arrive at work tired.

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Solution

If P then Q must have truth value in two cases

P true and Q true

P not true and Q true

So we see P not true can still imply Q true. So Q being true does not imply the truth of P

Here, P is the statemenet I drive to work

SO statement is incorrect because we cannot conclude from I arrive at work tired that I drive to work. I could have taken a bus. I may not have slept etc.