Conjectures and Counterexamples

Front

A concluding statement reached using inductive reasoning is called a _______

Back

conjecture

Front

Conjectures, like theorems, have been proven to be true.

Back

False

Front

For any right triangle, the sum of the squares of the legs is equal to the square of the hypothesis. This is an example of a conjecture.

Back

False

Front

No number of examples or cases can fully prove a conjecture.

Back

True

Front

A counterexample is an example that proves a conjecture to be true.

Back

False

Front

To fully disprove a conjecture, one needs to find only ONE counterexample.

Back

True

Front

Back

x = -2

Front

Back

a = 6

Front

Back

a = 4, b = 2

Front

Counterexample to: "Greg is a swimmer if and only if he is an athlete."

Back

Greg is an athlete and a basketball player.