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Which answers are examples of the Law of Detachment? Select each correct answer.

If two angles are linear pairs, the angles are supplementary. The two angles are linear pairs. Therefore, the angles are supplementary.

If an object is a square, it is a parallelogram. The object is a square. The object is a parallelogram.

If it is snowing, the play will be cancelled. It is snowing. Therefore, the play is cancelled.

If it is snowing, the play will be cancelled. If the play is cancelled, the theater will refund the cost of admission. Therefore, if it is snowing, the theater will refund the cost of admission to the play.

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Answers:

  A. If two angles are linear pairs, the angles are supplementary. The two angles are linear pairs. Therefore, the angles are supplementary.  

 B. If an object is a square, it is a parallelogram. The object is a square. The object is a parallelogram.

 C. If it is snowing, the play will be cancelled. It is snowing. Therefore, the play is cancelled.

  These are right.

Answer:

Law of detachment:

Statement 1: If a, then b

Statement 2: a

Conclusion: b

(A)

1. If two angles are linear pairs, then the angles are supplementary.

2. The two angles are linear pairs.

Let a be the statement " two angles are linear pairs"

let b be the statement "the angles are supplementary"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The angles are supplementary.

(B)

1. If an object is a square, then it is a parallelogram.

2. The object is a square.

Let a be the statement " an object is a square"

let b be the statement "The object is a square"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The object is a parallelogram.

(C)

1. If  it is snowing, then the play will be cancelled.

2. It is snowing.

Let a be the statement "it is snowing"

let b be the statement "the play will be cancelled"

then, 1 and 2 can be written as;

1. if a , then b

2. a

So, by the law of detachment we can deduce that b is true.

i.e, The play is cancelled.

Only option A, B and C  are examples of the Law of Detachment.





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