this subject is discrete structure c) Given the following argument: If 1 study,

Question

this subject is discrete structure

c) Given the following argument: If 1 study, then I will not fail mathematics. If I do not play computer games, then I will study. But I failed mathematics. Therefore I must have played computer games. Define 3 propositions from the above argument. You must label them as p, g, r. By using the propositions that you have defined in part (i) and logical connectives, translate the argument into 3 premises and a conclusion. i) ii) ii) Show that the argument is valid with formal reasoning.

Explanation / Answer

i) Let p be I will study, q be I will fail mathematics and r be I will play computer games.

ii) The given statements are

p -> ~q

~r -> p

q

---------------

r

iii)

1. Given: p -> ~q

2. Given: ~r -> p

3. Given: q

4. ~p

(Modus tollens of 1 and 3)

5. r

(Modus tollens of 4 and 5)

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