GATE CSE 2008 | Question: 15

Question

Which of the following tuple relational calculus expression(s) is/are equivalent to $\forall t \in r \left(P\left(t\right)\right)$?

1. $\neg \exists t \in r \left(P\left(t\right)\right)$
2. $\exists t \notin r \left(P\left(t\right)\right)$
3. $\neg \exists t \in r \left(\neg P\left(t\right)\right)$
4. $\exists t \notin r \left(\neg P\left(t\right)\right)$
   • A. I only
   • B. II only
   • C. III only
   • D. III and IV only

Comments

question says for all tuple t in r, t satisfies the condition.
It is equivalent to saying that there not exist any tuple t in r which do not satisfies the condition.

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Crucial point : A ∉ B = A ∈ B’

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Detailed Video Solution: https://youtu.be/7DodebRTM10 

Answer 1

∃t∈r(⌝ P(t))--means that there are some tuples in relation r which do not satisfy the constraint P(t)

and if we put not before this statement we get there are no tuples in relation r which do not satisfy the constraint P(t) which is equivalent to saying all tuples in relation r satify predicate condition P(t)

Comments

I think even (1) is same as yours.