Is an empty clause within another empty clause is equivalent to an empty clause ?(In CNF form)

Question

Is the clause { { } } ≡ { } ? The clauses are In CNF form.I tried thinking about it , so the final solution, according to me should be that the statement is true. Is the understanding correct?

Answer 1

It depends on the specific notation you are using (from a book? From lectures?) But in this context I would expect it to be:

1. { {} } is a conjunction of a single empty disjunction, which is is equivalent to that single empty disjunction, and its value is the identity element for disjunction (consider/remember what that is).

2. {} is the empty conjunction, its value is the identity element for conjunction.

Because these values are different, the clauses are not equivalent.