Q.1
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 _________
  • a) ∀nP ((n) → Q(n))
  • b) ∃ nP ((n) → Q(n))
  • c) ∀n~(P ((n)) → Q(n))
  • d) ∀nP ((n) → ~(Q(n)))
Q.2
Which of the following can only be used in disproving the statements?
  • a) Direct proof
  • b) Contrapositive proofs
  • c) Counter Example
  • d) Mathematical Induction
Q.3
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 ________
  • a) ∀nP ((n) → Q(n))
  • b) ∃ nP ((n) → Q(n))
  • c) ∀n~(P ((n)) → Q(n))
  • d) ∀n(~Q ((n)) → ~(P(n)))
Q.4
When to proof P→Q true, we proof P false, that type of proof is known as ___________
  • a) Direct proof
  • b) Contrapositive proofs
  • c) Vacuous proof
  • d) Mathematical Induction
Q.5
In proving √5 as irrational, we begin with assumption √5 is rational in which type of proof?
  • a) Direct proof
  • b) Proof by Contradiction
  • c) Vacuous proof
  • d) Mathematical Induction
Q.6
A proof covering all the possible cases, such type of proofs are known as ___________
  • a) Direct proof
  • b) Proof by Contradiction
  • c) Vacuous proof
  • d) Exhaustive proof
Q.7
Which of the arguments is not valid in proving sum of two odd number is not odd.
  • a) 3 + 3 = 6, hence true for all
  • b) 2n +1 + 2m +1 = 2(n+m+1) hence true for all
  • c) All of the mentioned
  • d) None of the mentioned
Q.8
A proof broken into distinct cases, where these cases cover all prospects, such proofs are known as ___________
  • a) Direct proof
  • b) Contrapositive proofs
  • c) Vacuous proof
  • d) Proof by cases
Q.9
A proof that p → q is true based on the fact that q is true, such proofs are known as ___________
  • a) Direct proof
  • b) Contrapositive proofs
  • c) Trivial proof
  • d) Proof by cases
Q.10
A theorem used to prove other theorems is known as _______________
  • a) Lemma
  • b) Corollary
  • c) Conjecture
  • d) None of the mentioned
0 h : 0 m : 1 s