Explain whether the following statement is a valid definition

Question

2. 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.

 

 

I dont get this question AT ALL. Please help!!

Answer 1

Hi Laila,

 

Well, I don't know what the basis of the question is, but I understand all the terms, anyway.

 

A definition is intended to establish a correspondence.  Therefore, we should have some notion of "this term applies if and only the definition is satisfied"  It's a name you can put on certain things.  Let's try defining "delicious" by the phrase "Pizzas are delicious."

 

Let's start with converse.  If a implies b, the converse is not b means not a.  So, for example, if all pizzas are delicious, then if something is not delicious, it can't be pizza, because all pizzas are delicious.

 

Similarly

 

If a 150º angle is an obtuse angle, then not an obtuse angle means not 150º.  That's actually true.  There's no problem on that front.

 

Biconditional.  Biconditional means a implies b AND b implies a.  This should be true of a definition.  So, we would have pizzas are delicious AND delicious things are pizzas.  But not all delicious things are pizzas, and we never said so.  All we said was that pizzas are delicious.  Nothing was said either way about hot fudge sundaes. So pizzas are delicious is not a definition.

 

Similarly, biconditional would mean a 150º angle is obtuse AND an obtuse angle is 150º.  But that's not true, and we never said it was. 

 

An Euler diagram would have a large circle of "all delicious things" and a smaller circle inside of "pizza".  If the two circles were the same, then "pizza" would be a definition.  But they aren't, so it isn't.

 

Similarly, "obtuse angles" is a set of stuff and "150º" is one angle in there. 

 

I hope that helps.

 

Regards,

Mike N.