law of detachment

[rachelmaddie]

In terms of providing geometric explanations and justification I’m not sure if I’ve answered this correctly for law of detachment.

The Law of Detachment states that if the hypothesis of a conditional statement is true, then the conclusion is also true.

If p —-> q is a true statement and p is true, then q is true which is read “if p, then q.”

Given: If Jillian gets a raise, then she will buy a new car. Jillian got a raise.

p = if Jillian gets a raise

q = then she will buy a new car

conclusion = Jillian got a raise.

Therefore, by the law of detachment, we can conclude that Jillian will also buy a new car.

 

[tkhunny]

No, "Jillian got a raise" is not the conclusion.

Given that "Jillian got a raise", we can know that she will "buy a new car".

We assume two things:
1) Jillian got a Raise (p)
2) If Jillian gets a Raise (p), she will buy a new car (q).

Given those two things, we conclude that she will buy a new car (q).

Thought question: If she buys a new car, can we conclude that she got a raise?

 

[rachelmaddie]

No, "Jillian got a raise" is not the conclusion.

Given that "Jillian got a raise", we can know that she will "buy a new car".

We assume two things:
1) Jillian got a Raise (p)
2) If Jillian gets a Raise (p), she will buy a new car (q).

Given those two things, we conclude that she will buy a new car (q).

Thought question: If she buys a new car, can we conclude that she got a raise?

Yes.

 

[tkhunny]

Yes.

Well, you'll have to look up the "Converse".

If she wins the lottery, she will buy a new car.
If she gets a massive tax refund, she will buy a new car.
If her great aunt Tillie leaves money in her will, she will buy a new car.

So, be careful with that. There may be other things that influence the conclusion.
Anyway, this isn't part of your question. Just something to keep in mind. It doesn't alway work both ways. It may be your responsibility to PROVE it, at times.

 

[rachelmaddie]

Well, you'll have to look up the "Converse".

If she wins the lottery, she will buy a new car.
If she gets a massive tax refund, she will buy a new car.
If her great aunt Tillie leaves money in her will, she will buy a new car.

So, be careful with that. There may be other things that influence the conclusion.
Anyway, this isn't part of your question. Just something to keep in mind. It doesn't alway work both ways. It may be your responsibility to PROVE it, at times.

The Law of Detachment states that if the hypothesis of a conditional statement is true, then the conclusion is also true.

If p —-> q is a true statement and p is true, then q is true which is read “if p, then q.”

Given: If Jillian gets a raise, then she will buy a new car. Jillian got a raise.

1) Jillian got a raise (p)

2) If Jillian gets a raise (p), then she will buy a new car (q).

Therefore, given those two statements, we conclude that she will buy a new car (q).

 

[Steven G]

The Law of Detachment states that if the hypothesis of a conditional statement is true, then the conclusion is also true.

If p —-> q is a true statement and p is true, then q is true which is read “if p, then q.”

Given: If Jillian gets a raise, then she will buy a new car. Jillian got a raise.

1) Jillian got a raise (p)

2) If Jillian gets a raise (p), then she will buy a new car (q).

Therefore, given those two statements, we conclude that she will buy a new car (q).

Better. What is in Bold above is NOT a conclusion but rather what is given.