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2. Explain whether the following statement is a valid definition: “A 150° angle

Algebra
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Explain whether the following statement is a valid definition: “A 150° angle is an obtuse angle.” Use the converse, biconditional, and at least one Euler diagram to support your answer.

Mar 18th, 2015

No, it is not a valid  definition

it is an imperative statement requiring you to do something!

As an obtuse angle can be defined as An angle that measures more than 90 degrees but less than 180 degrees.

“A 150° angle is an obtuse angle.” 

We will represent the proposition as follows: 
p=the angle is 150° 
q=it is an obtuse angle 

The above proposition (may or may not be true) is equivalent to: 
p->q (If the angle is 150°, it is an obtuse angle). 

The converse is 
q->p (If an angle is obtuse, it is 150°) 

NO IT DOES NOT FULFILL AS any angle between 90 degrees and 180 degrees is obtuse.

The biconditional is: 
p<->q (If the angle is 150°, it is an obtuse angle, and if an angle is obtuse, it is 150°) 

We can see that p->q is true,

 but q->p is not.

 Consequently p<->q is not true, because 
p<->q ≡ p->q ∧ q->p, 
so if q->p is false, p<->q is also false. 

The Euler diagram for p->q is a small circle P completely inside a bigger circle Q, so that whenever p is true, q has to be true. 

Reference 

  1. dictionary.reference.com/browse/obtuse+angle


Mar 19th, 2015

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