2C Practice: Counterexamples/Truth of Biconditionals

A counterexample is an example that proves a conjecture (or statement) to be true.

• True

• False

If it is a fraction, then it is a number between zero and one.  

What is an appropriate counterexample?

• $\frac{2}{3}$

• $\frac{4}{5}$
  

• $\frac{1}{2}$

• $\frac{3}{2}$
  

Which of the following is a counterexample to the following conjecture? 

If  $x^2\ =\ 4$ , then  $x=2$  .

• x = 4

• x = -2

• x = 2

• x = -4

If an animal is furry, then it is a hamster.

What would be an appropriate counterexample?

• goldfish

• frog

• elephant

• cat

If it is a number, then it is either positive or negative.

What is an appropriate counterexample?

• 10

• -2

• 0

• True. There is no counterexample.

Which is used to prove that a conjecture is false?

• Counterexample

• Inductive Reasoning

• Concluding statement

• Conjecture

Which of these is a counterexample to the following statement?

All vegetables are green.

• Banana

• Eggplant

• Green Beans

• Grass

The product of two negative numbers is greater than the sum of the two numbers.

What is an appropriate counterexample?

• -3 and -3

• True. There is no counterexample

• -1 and -1

• 4 and 6

What has to happen in order to write a true biconditional statement?

• conditional has to be true
• converse of the conditional has to be true
• BOTH converse and conditional must be true

• NEITHER has to be true

What phrase does a biconditional statement contain?

• if, then
• if, when
• if and only if
• then, if