NTA UGC NET DEC-2022 Paper-2
November 9, 2023Question 7829 – Theory-of-Computation
November 9, 2023UGC NET JRF November 2020 Paper-2
| Question 8 |
Consider the statement below.
A person who is radical (R) is electable (E) if he/she is conservative (C), but otherwise is not electable.
Few probable logical assertions of the above sentence are given below.,
Which of the above logical assertions are true?
Choose the correct answer from the options given below:
A person who is radical (R) is electable (E) if he/she is conservative (C), but otherwise is not electable.
Few probable logical assertions of the above sentence are given below.,
Which of the above logical assertions are true?
Choose the correct answer from the options given below:
| (B) only | |
| (C) only | |
| (A) and (C) only | |
| (B) and (D) only |
Question 8 Explanation:
1. (R ∧E) ↔C
This is not equivalent. It says that all (and only) conservatives are radical and electable.
2. R →(E ↔C)
This one is equivalent. if a person is a radical then they are electable if and only if they are conservative.
3. R →((C →E) ∨¬E)
This one is vacuous. It’s equivalent to ¬R ∨ (¬C ∨ E ∨ ¬E), which is true in all interpretations.
4.R ⇒ (E ⇐⇒ C) ≡ R ⇒ ((E ⇒ C) ∧ (C ⇒ E))
≡ ¬R ∨ ((¬E ∨ C) ∧ (¬C ∨ E))
≡ (¬R ∨ ¬E ∨ C) ∧ (¬R ∨ ¬C ∨ E))
This is not equivalent. It says that all (and only) conservatives are radical and electable.
2. R →(E ↔C)
This one is equivalent. if a person is a radical then they are electable if and only if they are conservative.
3. R →((C →E) ∨¬E)
This one is vacuous. It’s equivalent to ¬R ∨ (¬C ∨ E ∨ ¬E), which is true in all interpretations.
4.R ⇒ (E ⇐⇒ C) ≡ R ⇒ ((E ⇒ C) ∧ (C ⇒ E))
≡ ¬R ∨ ((¬E ∨ C) ∧ (¬C ∨ E))
≡ (¬R ∨ ¬E ∨ C) ∧ (¬R ∨ ¬C ∨ E))
Correct Answer: D
Question 8 Explanation:
1. (R ∧E) ↔C
This is not equivalent. It says that all (and only) conservatives are radical and electable.
2. R →(E ↔C)
This one is equivalent. if a person is a radical then they are electable if and only if they are conservative.
3. R →((C →E) ∨¬E)
This one is vacuous. It’s equivalent to ¬R ∨ (¬C ∨ E ∨ ¬E), which is true in all interpretations.
4.R ⇒ (E ⇐⇒ C) ≡ R ⇒ ((E ⇒ C) ∧ (C ⇒ E))
≡ ¬R ∨ ((¬E ∨ C) ∧ (¬C ∨ E))
≡ (¬R ∨ ¬E ∨ C) ∧ (¬R ∨ ¬C ∨ E))
This is not equivalent. It says that all (and only) conservatives are radical and electable.
2. R →(E ↔C)
This one is equivalent. if a person is a radical then they are electable if and only if they are conservative.
3. R →((C →E) ∨¬E)
This one is vacuous. It’s equivalent to ¬R ∨ (¬C ∨ E ∨ ¬E), which is true in all interpretations.
4.R ⇒ (E ⇐⇒ C) ≡ R ⇒ ((E ⇒ C) ∧ (C ⇒ E))
≡ ¬R ∨ ((¬E ∨ C) ∧ (¬C ∨ E))
≡ (¬R ∨ ¬E ∨ C) ∧ (¬R ∨ ¬C ∨ E))