Question

1. Using the Law of Syllogism, what conclusion can you draw from the following two statements?

Answer 1

These are 8 questions and 8 answers. Given that the answers exceeded the number of characters you can see all the answers in the file attached.

Question1. Using the Law of Syllogism, what conclusion can you draw from the following two statements?

If two angles are right angles, then they have the same measure.
If two angles have the same measure, then they are congruent.

Answer:

If two angles are right angles, then they are congruent.

Justification:

The law of sylllogism is a typy of logical reasoning used when there are two conditionals where the hypothesis of one is the conclusion of the other.

This is the scheme of the law of syllogism

statement    hypothesis  then   conclusion
   1                    p             →         q
   2                    q             →         r

Reasoning        p             →         r

As you see that is a kind of transitivity if p then q and if q then r implies if p then r.

Here you have:

p: if two angles are right angles
q: they  have the same measure
r: they are conngruent

So, from p → q and q → r, you can derive the conclusion p → r, which is if two angles are right angles they are congruent.


Qestion 2. Does the following argument illustrate the Law of Syllogism?

Given: If the power is cut, then the refrigerator will not work.
If the refrigerator will not work, then the food will spoil.

Conclude: If the power is cut, then the food will spoil.

Answer: yes

Justification:

As explained if the first answer, the law of syllogism permit to conncatenate two conditionals, where the conclusion of one is the hypothesis of the other permiting to conclude the validity of a third conditional through the reasoning:

first conditional:      if p then q
second contitional: if q then r

conclusion: if p then r.

In your question:

p: if the power is cut
q: the refrigerator will not work
r: the food will spoil

So, you have the exact structure of the syllogism law:

if the power is cut, then the refrigerator will not work
if the refrigerator will not work, then the food will spoil

Therefore, you conclude if the power is cut then the food will spoil.


Question 3. Does the following argument illustrate the Law of Detachment?

Given: If the fuse has blown, then the light will not go on.
The light will not go on.

Conclude: The fuse has blown.

Answer: no

Justification:

The law of detachment is the logical reasoning that permits you to derive the conclusion when the hypothesis on a conditional is true.

This is the scheme of the law of detachment:

conditional:                       if p , then q
hypothesis affirmation:     p is true

Conclusion: q is true

In this case:

The conditional is "if the fuse is blown, then the light will not go on:, so you are not affirming the hypothesis when you say "the light will not go on", which means that this is not the use of the law of detachment.

Question 4. Using the Law of Syllogism, what conclusion can you draw from the following two statements?

If it rains, then the roof leaks.
If the roof leaks, then the ceiling gets damaged.

Answer: If it rains, then the ceiling gets damaged.

Justification:

Law of syllogism:

conditional 1: if p then q
conditional 2: if q then r

conclusion: if p then r.

So, if it rains, then the roof leaks, and if the roof leaks, then the ceiling gets damaged, is the exactly the structure of the syllogism law that permits to conclude if it rains, then the ceiling gets damaged.

Question 5. Does the following argument illustrate the Law of Detachment?

Given: If the power has been cut, then the refrigerator does not work.
The power has been cut.

Conclude: The refrigerator does not work.

Answer: yes

Justification:

conditional:
if the power has ben cut, then the refrigerator does not work

hypothesis: if the power has been cut
conclusion: the refrigerator does not work

Reasoning: the hypothesis is affirmed (the power has been cut) then you conclude, by the detachment law, that the conclusion (the regrigerator does not work) is true.


Question 6. Use the Law of Detachment and the Law of Syllogism to draw a conclusion from the following true statements.

If you do not get enough sleep, then you will be tired.
If you are tired, then you cannot pay attention in school.

Answer:
Telling that you only got three hours of sleep on Tuesday is the affirmation of the hypothesis of the first statement: "you only got three hours of sleep on Tuesday night". So you can conclude by the detachment law the conclusion "you are tired on Tuesday".

Now, that the conclusion of the first statement has been proved, which is the hypothesis of the other conditional, by the law of syllogism the conclusion of the second conditional (you cannot pay attencion in school on Wednesday) has been proved.

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