Question

Use the logical quantifiers ∀ (for all), ∃ (exists), as well as ∧, ∨, ¬ and the arithmetic operations +, ×, =, >, < to write the following

An expression (,) such that for every natural numbers , , (, ) is true if and only if divides .

Answer 1

To express the statement 'for every natural numbers x and y, (x divides y) is true if and only if (x,y) is true' we can use logical quantifiers and arithmetic operations.

Step-by-step explanation:

To express the statement 'for every natural numbers x and y, (x divides y) is true if and only if (x,y) is true,' we can use logical quantifiers and arithmetic operations as follows:

∀x∀y((x divides y) ↔ (x=y×z) for some natural number z)

This expression states that for every natural numbers x and y, the statement 'x divides y' (x=y×z for some natural number z) is true if and only if (x,y) is true. The symbol '↔' represents the biconditional or if and only if operator.