Question

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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?

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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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-> The UGC NET Answer Key 2025 June was released on the official website ugcnet.nta.ac.in on 06th July 2025.

-> The UGC NET June 2025 exam will be conducted from 25th to 29th June 2025.

-> The UGC-NET exam takes place for 85 subjects, to determine the eligibility for 'Junior Research Fellowship’ and ‘Assistant Professor’ posts, as well as for PhD. admissions.

-> The exam is conducted bi-annually - in June and December cycles.

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