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Consider the statements: I. A ⇔  A ∨ ~ A II. A ⇔ A ∨ A III. A ∨ B ⇒ A IV. A ⇒ A ∨ B Which of the above refers to tautologies?

Consider the statements: I. A ⇔  A ∨ ~ A II. A ⇔ A ∨ A III. A ∨ B ⇒ A IV. A ⇒ A ∨ B Which of the above refers to tautologies? Correct Answer II and IV

The correct answer is option 4.

Concept:

Tautology:

 A tautology is a compound statement in Maths that always results in Truth value.

I. A ⇔  A ∨ ~ A:

False, not a tautology.

A            ~ A      A ∨ ~ A A ⇔  A ∨ ~ A
True False True True
False True True False

II. A ⇔ A ∨ A

True, The compound statement is a tautology.

A       A ∨ A A ⇔ A ∨ A
True True True
False False True

III. A ∨ B ⇒ A

False, not a tautology.

A       B      A ∨ B   A ∨ B ⇒ A
True True True True
True False True True
False True True False
False False False True

IV. A ⇒ A ∨ B

True, The compound statement is a tautology.

A       B      A ∨ B   A ⇒ A ∨ B
True True True True
True False True True
False True True True
False False False True

Hence the correct answer is II and IV.

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