Question

We are given the argument "If Dylan scores the first goal, he becomes man of the match. Either he scored the first goal or messi was injured. He didn't become man of the match this time. Therefore messi was injured.” The argument is valid.

• A. True
• B. False

Answer 1

The correct option is A

True

Lets denote the statements with symbols and analyse through a truthtable the possible truth value the statement can take.

Once we do that we will be in a position to comment about the argument.

Let,

p $\to$ Dylan scores the first goal

q $\to$ Dylan becomes man of the match

r $\to$ Messi is injured

The assumptions in the argument are, 1)p $\to$ q$\equiv$ S1

2)p v r$\equiv$ S2

3)$\sim$q$\equiv$ S3

Conclusion is r $\equiv$ S

Given argument is $S_1,S_2,S_3$ gives S.

Lets construct the truth table.

$\begin{array}{ccc}pqr& S_1{S}_2{S}_3& S\\ & p\to qp\vee r\sim q& \left(r\right)\\ TTT& TTF& T\\ TTF& TTF& F\\ TFT& FTT& T\\ TFF& FTT& F\\ FTT& TTF& T\\ FTF& TFF& F\\ FFT& TTT& T\\ \cdots \cdots \cdots & \cdots \cdots \cdots & \cdots \\ FFF& TFT& F\end{array}$

The argument is valid when on the situation where all the assumptions are true the truth value of the conclusion should be TRUE for the argument to be true. This is the case here from $7^{th}$ row. $\therefore$ Argument is valid.