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Consider the following propositions:
(i) (~p → ~q) → (q → p)
(ii) [p ∧ (p∧~q∨~r∧s ∨ q∧r∧s ∨p) →~r] → (r→~p)
(iii) (p → q) ∧ (~p → ~q) → (p ↔ q)
Which of the above proposition/s is/are a tautology?
  • a)
    (i) only
  • b)
    Both (i) and (ii)
  • c)
    All these
  • d)
    Both (i) and (iii)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider the following propositions:(i) (~p → ~q) → (q &rarr...
(i) Tautology: Because contrapositive of an implication always follows from it.
(ii) Tautology: LHS is nothing but p→~r which in turn implies RHS.
(iii) Tautology: (p → q) ∧ (q → p) ≡ (p ↔ q)
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Most Upvoted Answer
Consider the following propositions:(i) (~p → ~q) → (q &rarr...
(i) (~p
(ii) (q ∧ ~r)
(iii) (p ∨ q)
(iv) (~r ∨ ~s)

The propositions given are:
(i) (~p
(ii) (q ∧ ~r)
(iii) (p ∨ q)
(iv) (~r ∨ ~s)
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Consider the following propositions:(i) (~p → ~q) → (q → p)(ii) [p ∧ (p∧~q∨~r∧s ∨ q∧r∧s ∨p) →~r] → (r→~p)(iii) (p → q) ∧ (~p → ~q) → (p ↔ q)Which of the above proposition/s is/are a tautology?a)(i) onlyb)Both (i) and (ii)c)All thesed)Both (i) and (iii)Correct answer is option 'C'. Can you explain this answer?
Question Description
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