# Which statement is false? A. every irrational number is also a real number. B. every integer is also a real number. C. no irrational number is irrational. D. every integer is also an irrational number.

Question
Irrational numbers
Which statement is false?
A. every irrational number is also a real number.
B. every integer is also a real number.
C. no irrational number is irrational.
D. every integer is also an irrational number.

2021-02-22
The set of real numbers include integers, rational numbers, and irrational numbers. This then implies that all irrational numbers and integers are also real numbers and thus statement A and B are correct.
The rational numbers are all numbers that can be written as the division of two integers, which thus also include all integers. The set of irrational numbers then contains all real numbers that are NOT rational numbers and thus the set of irrational numbers do not include integers, which implies that statement D is false.

### Relevant Questions

True or False?
1) Let x and y real numbers. If $$\displaystyle{x}^{{2}}-{5}{x}={y}^{{2}}-{5}{y}$$ and $$\displaystyle{x}\ne{y}$$, then x+y is five.
2) The real number pi can be expressed as a repeating decimal.
3) If an irrational number is divided by a nonzero integer the result is irrational.
Writing and Proof: If true prove it, if false give a counterexample. Use contradiction when proving.
(a) For each positive real number x, if x is irrational, then $$\displaystyle{x}^{{2}}$$ is irrational.
(b) For every pair of real numbers a nd y, if x+y is irrational, then x if irrational or y is irrational
In which set(s) of numbers would you find the number $$\displaystyle\sqrt{{80}}$$
- irrational number
- whole number
- rational number
- integer
- real number
- natural number
Given each set of numbers, list the
a) natural Numbers
b) whole numbers
c) integers
d) rational numbers
e) irrational numbers
f) real numbers
$$\displaystyle{\left\lbrace-{6},\sqrt{{23}},{21},{5.62},{0.4},{3}\frac{{2}}{{9}},{0},-\frac{{7}}{{8}},{2.074816}\ldots\right\rbrace}$$
Determine whether the below given statement is true or false. If the statement is false, make the necessary changes to produce a true statement:
All irrational numbers satisfy |x - 4| > 0.
The rational numbers are dense in $$\displaystyle\mathbb{R}$$. This means that between any two real numbers a and b with a < b, there exists a rational number q such that a < q < b. Using this fact, establish that the irrational numbers are dense in $$\displaystyle\mathbb{R}$$ as well.
Discover prove: Combining Rational and Irrationalnumbers is $$\displaystyle{1.2}+\sqrt{{2}}$$ rational or irrational? Is $$\displaystyle\frac{{1}}{{2}}\cdot\sqrt{{2}}$$ rational or irrational? Experiment with sums and products of ther rational and irrational numbers. Prove the followinf.
(a) The sum of rational number r and an irrational number t is irrational.
(b) The product of a rational number r and an irrational number t is irrational.
Which of the following is/are always false ?
(a) A quadratic equation with rational coefficients has zero or two irrational roots.
(b) A quadratic equation with real coefficients has zero or two non - real roots
(c) A quadratic equation with irrational coefficients has zero or two rational roots.
(d) A quadratic equation with integer coefficients has zero or two irrational roots.
$$\displaystyle{3}\frac{{1}}{{7}}$$ and $$\displaystyle{3}\frac{{1}}{{6}}$$