Question

Express, “The difference of a real number and itself is zero” using required operators.

(a) ∀x(x − x! = 0)

(b) ∀x(x − x = 0)

(c) ∀x∀y(x − y = 0)

(d) ∃x(x − x = 0)

The question was asked in a national level competition.

Enquiry is from Logics topic in portion The Foundation: Logics and Proofs of Discrete Mathematics

Answer 1

Correct choice is (b) ∀x(x − x = 0)

To explain I would say: For every real number x, difference with itself is always zero.