Test the validity of the following argument?

Question

If Nomi studies then he will not fail in mathematics

2. If he does not play basket ball then he will study

3. But he failed in mathematics

4. Therefore he played basket ball

Answer: p q r format only

Answer 1

Don't know the pqr format, but the argument is true.

3 states that he failed, 1 states that he could not have failed had he studied, therefore, he did not study.

2 states that if he did anything other that playing basketball, he would be studying. Because we already know he was not studying, he could have done nothing other than playing basketball. Basketball being the only thing other than studying he could have done.

Hope it helps.

Answer 2

he failed mathematics

so from 1 he did not study

so from 2 he did play basketball

QED