4. (6 pts) State the inverse, converse and contrapositve of the following implic

Question

4. (6 pts) State the inverse, converse and contrapositve of the following implication: If I debug the code or someone tests the program then the program does not have problems. Inverse Converse: Contrapositive: 5. (4 pts) Explain whether or not the following is a valid argument. If it is valid, show that it is valid using the inference rules. If it is invalid, explain what makes it invalid. If I train hard then I race in the Olympics. If I am sick then I do not go to the Pan Am Games. If I do not train hard then I do not go to the Pan Am Games. I am sick. Therefore I do not train hard.

Explanation / Answer

4.In the above statement:

Hypothesis is if I debug the code or someone tests the program
Conclusion: The program does not have problem

It is coverse. It can't be inverse because in inverse hypothesis and conclusion are
both negated and contrapositive is just interchanging hypothesis and concluion
of inverse. Here only conclusion is negated not the hypothesis.

5.
T - I traing hard
O - I race in olympics
P - I go to Pan Am games
S - I am sick

1.T -> O
2.S -> not P
3.not T -> not P

4.S
Conclusion: not T

Proof:

With Modes ponens 2 & 4 we get not P

Now with hypothetical Syllogism on not P and 3
we get not T

Hence proved and statement is valid.

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