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Consider the following statements :

(a) False ? True

(b) If α ? (β ∧ γ) then α ? β and α ? γ.

Which of the following is correct with respect to the above statements?

This question was previously asked in
UGC NET Computer Science (Paper 2) July 2018 Paper
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  1. Both statement (a) and statement (b) are false.
  2. Statement (a) is true but statement (b) is false.
  3. Statement (a) is false but statement (b) is true.
  4. Both statement (a) and statement (b) are true.

Answer (Detailed Solution Below)

Option 4 : Both statement (a) and statement (b) are true.
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Detailed Solution

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(a) False ? True

It can be rewritten as : False V True

Truth table for OR:

A

B

A V B

True

True

True

True

False

True

False

True

True

False

False

False

 

So, false ? true results in true.

(b) If α ? (β ∧ γ) then α ? β and α ? γ.

It can be rewritten as : α V (β ∧ γ) , (α V β ) ∧ (α V γ)

Truth table for this:

α

β

γ

α V β

α V γ

β ∧ γ

α V (β ∧ γ)

(α V β ) ∧ (α V γ)

True

True

True

True

True

True

True

True

True

True

False

True

True

False

True

True

True

False

True

True

True

False

True

True

True

False

False

True

True

False

True

True

False

True

True

True

True

True

True

True

False

True

False

True

False

False

False

False

False

False

True

False

True

False

False

False

False

False

False

false

false

false

false

false

 

Here if α V (β ∧ γ) is true then (α V β ) ∧ (α V γ) is true.

And if α V (β ∧ γ) is false then (α V β ) ∧ (α V γ) is false.

So, given statement is true.
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