Question

Suppose that we add a new quantifier called exists unique to first- (d) order logic, using the symbol 3! to represent it. It means that there is exactly one element of the universe that satisfies the subsequent formula. In this question, variables will range over the universe of numbers. [1 mark] (0) Is 3!x. x + x 2 valid? Why? Give an example of a valid formula that uses the quantifier, and an example of an unsatisfiable one. Both must be different from the formula from (i) above. (ii) 2 marks) (ii) For any formula f that refers to x, we can express 3!x. f using only the ordinary universal and existential quantifiers. Give a formula using f, 3, and V, but not 3! that has the same semantics as 3!x. f. (Hint: you can use a formula g which is the same as f, but using variable y instead of x.) 2 marks]

Answer 1

12x 2. not '스