GATE 2008
March 14, 2025GATE 2008
March 14, 2025GATE 2008
| Question 15 |
Which of the following tuple relational calculus expression(s) is/are equivalent to ∀t ∈ r(P(t))?
- I. ¬∃t ∈ r(P(t))
II. ∃t ∉ r(P(t))
III. ¬∃t ∈ r(¬P(t))
IV. ∃t ∉ r(¬P(t))
| I only | |
| II only | |
| III only | |
| III and IV only |
Question 15 Explanation:
Demorgan law:
∀xP(x) ≡ ∼∃x(∼P(x))
∼∀x(∼P(x)) ≡ ∃x(P(x))
Given: ∀t ∈ r(P(t))—— (1)
As per Demorgan law
(1) ⇒ ∼∃t ∈ r(∼P(t))
which is option (III).
∀xP(x) ≡ ∼∃x(∼P(x))
∼∀x(∼P(x)) ≡ ∃x(P(x))
Given: ∀t ∈ r(P(t))—— (1)
As per Demorgan law
(1) ⇒ ∼∃t ∈ r(∼P(t))
which is option (III).
Correct Answer: C
Question 15 Explanation:
Demorgan law:
∀xP(x) ≡ ∼∃x(∼P(x))
∼∀x(∼P(x)) ≡ ∃x(P(x))
Given: ∀t ∈ r(P(t))—— (1)
As per Demorgan law
(1) ⇒ ∼∃t ∈ r(∼P(t))
which is option (III).
∀xP(x) ≡ ∼∃x(∼P(x))
∼∀x(∼P(x)) ≡ ∃x(P(x))
Given: ∀t ∈ r(P(t))—— (1)
As per Demorgan law
(1) ⇒ ∼∃t ∈ r(∼P(t))
which is option (III).