Question

Prove or disprove these universally quantified statements. If disproving, you must provide a counterexample, where the domain for all variables consists of all real numbers. ∀x, ∃y,(x=1/y).

a) True
b) False

Answer 1

For any real number x, the existence of y= 1/x ensures x=1/y, validating the universally quantified statement. The statement is true

Step-by-step explanation:

The statement ∀x, ∃y,(x = 1/y) is True.

This statement asserts that for every real number x, there exists a real number y such that x is equal to 1 divided by y.

To prove this statement, we can solve for y in terms of x.

If we,

let y=1/x , then 1/y = 1/1/x =x .

Therefore, for any real number x, we can find a corresponding real number y such that x = 1/y.

So, the statement is true.