Question

Which statement is false?

Every integer is a real number.
Every real number is a rational number.
Every positive rational number has a square root.
Every integer is a rational number.

Answer 1

Every positive integer is a rational number

Answer 2

Every real number is a rational number (False)

Explanation:

A Rational Number is a number that can be written in this form
`(a)/(b)` such b≠0. But in the Real Set, there is other subset like the Irrational set whose elements cannot be written in p/q form such as
`√(2)`,
`\pi`, etc. Those numbers can't be written as a ratio p/q.

So it is false to say that Every Real number is a rational number, for Irrational numbers are not Rational ones.