Question

Rewrite the following statement formally. Use variables and

include both quantifiers ∀ and ∃ in your answer. Every rational
number can be written as a ratio of some two integers.

Answer 1

Let R(x) be the predicate "x is a rational number," I(x, y) be the predicate "x can be written as a ratio of two integers," and Q(x, y) be the quantifier "x, y are integers."

The formal statement can be written as follows:

∀x (R(x) → ∃y∃z (Q(y, z) ∧ I(x, y/z)))

This statement can be read as: "For every x, if x is a rational number, then there exist y and z (which are integers) such that y divided by z is a ratio that can represent x."

Explanation: