Which of the following is a tautology?
2018
Which of the following is a tautology?
- A.
a∨b→b∧c
- B.
a∧b→b∨c
- C.
a∨b→(b→c)
- D.
None of the above
Attempted by 190 students.
Show answer & explanation
Correct answer: B
Definition: A tautology is a formula that is true for every possible assignment of truth values to its propositional variables.
Expression a∨b → b∧c: Not a tautology. Counterexample: a = true, b = false, c = false. Then a∨b = true but b∧c = false, so the implication is false.
Expression a∧b → b∨c: This is a tautology. Reason: if a∧b is true then b is true, and therefore b∨c is true. Thus whenever the antecedent holds the consequent holds, so the implication is true for every assignment.
Expression a∨b → (b → c): Not a tautology. Counterexample: a = true, b = true, c = false. Then a∨b = true but b → c = false, so the implication is false.
Option 'None of the above': Incorrect because the formula a∧b → b∨c is a tautology.
Conclusion: The tautology among the given formulas is a∧b → b∨c.