Question

Which of the diagrams below represents the contrapositive of the statement, "If it is a triangle, then it has three vertices"

A. Figure A
B. Figure B

(Picture below)

Answer 1

any guesses and why you think its the answer?

Answer 2

I'd say figure A because contrapositive is just the opposite of the saying right?

Answer 3

@completeidiot

Answer 4

Contrapositive is logically equivalent (means the same thing) as the original statement.

Answer 5

Right, so it's figure A?
because it says if it's not a triangle than it doesn't have three vertices.
And the original says that triangles do have three vertices.

Answer 6

A is the inverse because all it is doing is negating the premise and conclusion.

Answer 7

So it's like saying the same thing.

Answer 8

But in a different way.

Answer 9

Or I'm wrong?

Answer 10

This is a little tricky because the original statement is a definition of sorts, so it's biconditional - that means that it is equivalent to its converse, and since the converse and inverse are equivalent, then the inverse and contrapositive will be equivalent.

Answer 11

correct me if im wrong, wouldnt the contrapositive statement be

if it doesnt have 3 vertices, then its not a triangle?

Answer 12

Here's the symbolic layout.
a=premise, b=conclusion
Conditional: a-->b
Converse: b-->a
Inverse: not a --> not b
Contrapositive: not b --> not a

Conditional = Contrapositive
Converse = Inverse

If biconditional, then Conditional = Converse, etc.

Answer 13

Hmmm, am I reading the direction of the sets wrong? I think I am.. oops. The inner circle is the premise and the outer circle is the conclusion.

Answer 14

Yeah, sorry, you were right. It is A because if you are in the set of things that don't have 3 vertices, then you have to be in the set of things which are not triangles.
I didn't consider the overlapping sets consideration enough and was operating just with the symbols.

Answer 15

Figure B doesn't make sense because it can't be a triangle an not have three vertices, but it's possible for something to have three vertices and not be a triangle.

Answer 16

Thank you very much for taking the time to explain everything!
It has helped me a lot.

Answer 17

My pleasure. This world could definitely use more logical thinkers!