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GO Classes 2023 | Weekly Quiz 5 | Question: 8

GO Classes asked in Mathematical Logic Mar 30, 2022 edited Apr 26, 2022 by Lakshman Bhaiya

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Consider the following arguments.

$\text{Argument 1:}$ If it does not rain or it is not foggy, then the sailing race will be held, and life-saving demonstrations will go on. If the sailing race is held, then the trophy will be awarded. The trophy was not awarded. Therefore, it rained.

$\text{Argument 2:}$ The attack will succeed only if the enemy is taken by surprise or the position is weakly defended. The enemy will not be taken by surprise unless he is overconfident. The enemy will not be overconfident if the position is weakly defended. Therefore, the attack will not succeed.

Which of the following is true?

Only Argument $1$ is valid.
Only Argument $2$ is valid.
Both Arguments are valid.
No Argument is valid.

GO Classes asked in Mathematical Logic Mar 30, 2022 edited Apr 26, 2022 by Lakshman Bhaiya

643 views

4 Comments

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by Abhrajyoti00

commented Oct 9, 2022

@JAINchiNMay Actually if the 3 conditions are met, then it rained as well as it was foggy. This will help you:-

rain’+fog’ → race . life (i)

race → trophy (ii)

trophy’ (iii)

Eqn (ii) can be rewritten as : trophy’ → race’ [if no trophy then no race, contrapositive]

It is given in eqn (iii) that there was not trophy. [Hence we can conclude no race] (iv)

Now eqn (i) can be rewritten as: (race . life)’ → (rain’ + fog’)’

or, race’ + life’ → rain . fog [ means, if either no race or no life saving, then both rain and fog]

And we already concluded no race in eqn (iv), hence there was both rain and fog.

Option A.

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