Let the statement be “If n is not an odd integer then square of n is not odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof we should prove _________

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

Let the statement be “If n is not an odd integer then sum of n with some not odd number will not be odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “sum of n with some not odd number will not be odd.” A proof by contraposition will be ________

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

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

A proof covering all the possible cases, such type of proofs are known as ___________

Which of the arguments is not valid in proving sum of two odd number is not odd.

A proof broken into distinct cases, where these cases cover all prospects, such proofs are known as ___________

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

A theorem used to prove other theorems is known as _______________