# Logic and Proof

# Logic and Proof: Make a (Mathematical) Statement Quiz

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Logic and Proof**Q. Is the statement "1 + 1 = 2 or any two points determine a line" true or false?

True

False

Both true and false

Not enough information

All of the above

Q. What is the converse of

*r*→*z*?*r*→

*z*

*z*→

*r*

not

*z*→ not*r**r*→ not

*r*

not

*r*→ not*z*Q. Which of "and," "not," and "or" link two statements together?

"and"

"or"

"not"

"and" and "or"

"and," "not," and "or"

Q. How many values of

*x*make the statement "*x*≤ 5 and*x*≥ 5" true?None

1

2

5

Infinitely many

Q. Suppose we know

*a*→*b*,*b*→*c*. If we know*b*is true, may we infer*c*?No

Yes, by detachment

Yes, by syllogism

Yes, by transitivity

Yes, by reflexivity

Q. Is the contrapositive of "Everything brown is a dog" true?

No, and a white dog is a counterexample

No, and a brown hat is a counterexample

No, and a white hat is a counterexample

No, and a brown dog is a counterexample

Yes

Q. Which is an example of something "white or not soft?"

Pink cotton ball

Blue bunny rabbit

Gray moldy marshmallow

White rock candy

Green pillow

Q. Suppose that

*p*→*q*and*p*→*r*. May we infer that*q*→*r*?Yes, by detachment

Yes, by symmetry

Yes, by syllogism

Yes, by addition

No

Q. What is the converse of not

*p*→ not*q*?*p*→

*q*

not

*q*→ not*p**q*→

*p*

not

*p*→*q**p*→ not

*q*

Q. The statements

*p*→*q*and*q*→*r*are given. If we know*q*to be true, which of the following CANNOT be assumed as true?*p*

*p*→

*q*

*q*

*q*→

*r*

*r*