Question

Read the following two statements. Then use the Law of Syllogism to draw a conclusion.

If the TV is too loud, then it will give me a headache.
If I have a headache, then I will have to rest.

a) If the TV is too loud, then I will have to rest.
b) If the TV is too loud, then I will not have to rest.
c) If the TV is not too loud, then I will have a headache.
d) If the TV is not too loud, then I will not have to rest.

Answer 1

Using the Law of Syllogism, combining the two statements, 'If the TV is too loud, then it will give me a headache' and 'If I have a headache, then I will have to rest,' leads to the conclusion: 'If the TV is too loud, then I will have to rest.'

Step-by-step explanation:

The Law of Syllogism helps us draw logical conclusions based on two related conditional statements. In this case, we have:

1. If the TV is too loud, then it will give me a headache.
2. If I have a headache, then I will have to rest.

By applying the Law of Syllogism, we can combine these statements to reach a new conclusion:

If the TV is too loud (first condition), then it will give me a headache (second condition). And, if I have a headache (second condition), then I will have to rest (final result).

Therefore, the correct conclusion using the Law of Syllogism is: If the TV is too loud, then I will have to rest.

None of the other options logically follow from the given statements. Options b), c), and d) do not use the Law of Syllogism and either introduce negations or unrelated premises.