Are the following arguments valid or invalid, and how do I go about figuring out

Question

Are the following arguments valid or invalid, and how do I go about figuring out the answers for these?

1.

Is the following argument valid or invalid (exercise 5.3)?

Premise: ~(P v Q)

Thus,

Conclusion: ~P

2.

Is the following argument valid or invalid (exercise 5.4)?

Premise 1: ~(P & Q)

Premise 2: P

Thus,

Conclusion: ~Q

3.

Is the following argument valid or invalid (exercise 5.5)?

Premise: ~(P & Q)

Thus,

Conclusion: ~P

4.

Is the following argument valid or invalid (exercise 5.6)?

Premise 1: P & Q

Premise 2: ~P

Thus,

Conclusion: R

Explanation / Answer

Procedure: Simply make a truth table for premise and conclusion then to confirm if the argument is valid simply verify if the conclusion is true when premise is true.

Solution 1:

Argument is valid since our conclusion is true when premise is true.

Solution 2:

This argumnt is invalid since in third row conclusion is false even if premise is true.

Solution 3:

This argumnt is invalid since in fourth row conclusion is false even if premise is true.

Solution 4:

Here no row is there when both premise are true hence our conclusion doesnt depend on premises.

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