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.

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