Question

Use truth table to test the validity of:
If I study, then I will not fail mathematics
if I don't play basketball, then I will study
But I failed mathematics
Therefore I must have played basketball

Answer 1

Answer on Question #69499 – Math – Discrete Mathematics

Use truth table to test the validity of:

If I study, then I will not fail mathematics

if I don't play basketball, then I will study

But I failed mathematics

Therefore I must have played basketball.

Solution:

A – Fail mathematics

B – Play basketball

C – Study.

-> - implication

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

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

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

$C \rightarrow \overline{1} = C \rightarrow 0 = \overline{C} = 1 => C = 0$

$\overline{B} \rightarrow 0 = B = 1$

That means, that he must have played basketball.

Answer: True.

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