Proof

Which of the following can only be used in disproving the statements?

• Direct proof

• Contrapositive proofs

• Counter Example

• Mathematical Induction

When to proof P→Q true, we proof P false, that type of proof is known as ___________.

• Direct proof

• Contrapositive proofs

• Vacuous proof

• Mathematical Induction

In proving √5 as irrational, we begin with assumption √5 is rational in which type of proof?

• Direct proof

• Contrapositive proofs

• Vacuous proof

• Mathematical Induction

A proof that p → q is true based on the fact that q is true, such proofs are known as ___________.

• Direct proof

• Contrapositive proofs

• Trivial proof

• Proof by cases

It is an argument that establishes a true statement.

• proof

• direct

• indirect

• methods

By direct proof, we assume that p is __________ and prove that q is true.

• true

• even

• false

• odd

In indirect proof, the _______ of the implication "if p then q" is considered.

• inverse

• transpose

• converse

• contrapositive

Which of the following is correct?

• proof by contradiction is a direct proof method

• An irrational number can be defined as   where a and b are integers, such that b 0.

• A proof by contraposition for p→q is done by proving ∼p→∼q.

• A number divisible by k can be represented as n∣k.

Tags

CCSS.8.NS.A.1

Using the direct proof, what can be assumed so that the statement below is true?

If an integer is odd and another integer is even, their product is even.

• The integers are both odd.

• An integer is odd and another integer is even

• The integers are both even.

• Neither of them is odd nor even.

Using the indirect proof, what can be assumed so that the statement below is true? If the square of an integer n is even, then n itself is even.

• n is odd

• n is neither odd nor even

• n is even

• n is both even and odd