SETS AND SUBSETS OF REAL NUMBERS WORKSHEET

Question 1 : 

Tell whether the given statement is true or false. Explain your choice.

"All irrational numbers are real numbers"

Question 2 : 

Tell whether the given statement is true or false. Explain your choice.

"No rational numbers are whole numbers"

Question 3 : 

Tell whether the given statement is true or false. Explain your choice.

"All rational numbers are integers"

Question 4 : 

Tell whether the given statement is true or false. Explain your choice.

"Some irrational numbers are integers"

Question 5 : 

Tell whether the given statement is true or false. Explain your choice.

"All whole numbers are rational numbers"

Question 6 : 

Tell whether the given statement is true or false. Explain your choice.

"No irrational numbers are whole numbers"

Answers

1. Answer :

"All irrational numbers are real numbers"

True

Every irrational number is included in the set of real numbers. The irrational numbers are a subset of the real numbers.

2. Answer :

"No rational numbers are whole numbers"

False

A whole number can be written as a fraction with a denominator of 1, so every whole number is included in the set of rational numbers. The whole numbers are a subset of the rational numbers.

3. Answer :

"All rational numbers are integers"

False

Every integer is a rational number, but not every rational number is an integer.

For example, rational numbers such as 3/5 and -5/2 are not integers. 

4. Answer :

"Some irrational numbers are integers"

False

Real numbers are either rational or irrational numbers.

Integers are rational numbers, so no integers are irrational numbers.

5. Answer :

"All whole numbers are rational numbers"

True

Whole numbers are a subset of the set of rational numbers and can be written as a ratio of the whole number to 1.

6. Answer :

"No irrational numbers are whole numbers"

True

All whole numbers are rational numbers.

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