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If statement (3) follows from statements (1) and (2) by the Law of Detachment or Law...

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novjb | Salutatorian

Posted June 19, 2013 at 11:14 PM via web

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If statement (3) follows from statements (1) and (2) by the Law of Detachment or Law of Syllogism then state the law that was used(if any).

1.  (1)If Janet finishes her homework, then she will get to watch TV.

(2) Janet finished her homework.

(3) Janet gets to watch TV.

I think the answer is the law of Detachment

 

2. (1) If Janet watches TV, then she will eat pretzels.

(2)If Janet finishes her homework, then she will watch TV.

(3)If Janet finishes her homework, then she will eat pretzels.

I think the answer is the law of syllogism

3. (1) If Janet watches TV, then she will eat pretzels.

(2) Janet ate some pretzels.

(3)Janet got to watch TV.

I think the answer is neither.

Thank you in advance:)

Tagged with geomerty, laws, laws of logic, math

1 Answer | Add Yours

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted June 20, 2013 at 4:57 AM (Answer #1)

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(1) The law of detachment takes the form:

1. If P then Q

2. P

3. Q

The conditional (If P then Q) is if Janet finishes her homework then she gets to watch TV.

The hypothesis P is that Janet has finished her homework.

The conclusion Q is that Janet can watch TV.

This is an example of the Law of Detachment (or Modus ponens or affirming the antecedent.)

(2) The Law of syllogism is of the form:

1. If P then Q

2. If Q then R

3. If P then R

The first conditional has the hypothesis P Janet watches TV and the conclusion Q that Janet eats pretzels.

The second conditional has the hypothesis R that Janet finishes her homework and conclusion P that Janet watches TV.

The third conditional has hypothesis R janet finishes her homework and conclusion Q that Janet eats pretzels.

This is the Law of Syllogism

(3) This is neither. We have taken the conclusion of the conditional and used it as the hypothesis which yields no valid conclusion.

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