Basic Math Proof Techniques Quiz

What is a mathematical statement?

• A statement that has no truth value

• A statement that is always true

• A statement that is either true or false

• A statement that can be both true and false

Which of the following is a true statement?

• 6 is an even integer

• 1 + 1 = 10

• 10 is an odd integer

• The moon is flat

What does the logical operator 'AND' represent?

• ∨

• →

• ∧

• ¬

What is the symbol for 'There exists'?

• ¬

• ∧

• ∃

• ∀

Which proof technique assumes the opposite of what you want to prove?

• Direct Proof

• Proof by Induction

• Proof by Contradiction

• Proof by Contrapositive

What is the definition of an even integer?

• n = 2k + 1

• n = 2k

• n = k + 1

• n = 2k - 1

In a direct proof, what is the first step?

• Assume P is true

• Assume Q is true

• Show a contradiction

• Use induction

What is the contrapositive of P → Q?

• Q → P

• ¬P → ¬Q

• P → ¬Q

• ¬Q → ¬P

What is the basis case in proof by induction?

• The first case to prove

• The last case to prove

• The case where n = 0

• The case where n = 1

What does the statement 'The sum of any two consecutive numbers is odd' imply?

• ¬P → ¬Q

• Q → P

• P ↔ Q

• P → Q