Check the validity of the following argument: “If I study then I will not fail in Mathematics. If I do not play Basket ball then I will study. I failed in Mathematics. Therefore I must have played Basketball

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A – Fail mathematics

B – Play basketball

C – Study.

-> - implication

$\def\arraystretch{1.5} \begin{array}{c:c:c:c} A & C\to\bar{A} & \bar{B}\to C & B \\ \hdashline 1 & 1 & 1 & ? \end{array}$

If I study, then I will not fail mathematics <=> $C\to\bar{A}=1$

if I don't play basketball, then I will study <=> $\bar{B}\to C =1$

But I failed mathematics <=> $A=1$

$C\to\bar{1}=C\to0=\bar{C}=1=>C=0$

$\bar{B}\to0=B=1$

That means that he must have played basketball.

True.