Let’s go through each statement one by one and decide if it’s TRUE or FALSE. We’ll use simple definitions to help us.
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1. All counting numbers are integers.
Counting numbers = 1, 2, 3, 4, ... (also called natural numbers)
Integers include all whole numbers and their negatives: ..., -3, -2, -1, 0, 1, 2, 3, ...
So yes — every counting number is also an integer.
✔ TRUE
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2. The integer 8 can be expressed as a fraction.
Any integer can be written as itself over 1 → 8 = 8/1
Fractions don’t have to be “parts” — they can represent whole numbers too.
✔ TRUE
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3. Non-repeating, non-terminating decimals are irrational.
Irrational numbers are decimals that never end AND never repeat (like π or √2).
Rational numbers either terminate or repeat.
So this matches the definition of irrational.
✔ TRUE
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4. Whole numbers exclude zero.
Whole numbers = 0, 1, 2, 3, ...
Zero IS included in whole numbers.
✘ So saying they “exclude zero” is wrong.
✔ FALSE
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5. The number 3.35 is a rational number.
3.35 ends after two decimal places → it terminates.
Terminating decimals are always rational.
Also, 3.35 = 335/100 → which is a fraction.
✔ TRUE
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6. Irrational numbers are not included in the number line.
All real numbers — including irrationals — live on the number line.
For example, √2 is between 1 and 2 on the number line.
✘ So this is false.
✔ FALSE
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7. The largest negative integer is –1.
Negative integers: -1, -2, -3, ...
–1 is closest to zero → so it’s the biggest (least negative).
✔ TRUE
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8. Zero is a positive integer.
Positive means greater than zero.
Zero is neither positive nor negative.
✘ So this is false.
✔ FALSE
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9. The union of the set of rational numbers and the set of irrational numbers is the set of real numbers.
Real numbers = everything you can put on the number line.
That includes both rationals (fractions, terminating/repeating decimals) and irrationals (non-repeating, non-terminating).
Together, they make up ALL real numbers.
✔ TRUE
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10. The intersection of the set of positive integers and the set of negative integers is an empty set.
Positive integers: 1, 2, 3, ...
Negative integers: -1, -2, -3, ...
No number is both positive and negative.
So there’s nothing in common → empty set.
✔ TRUE
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Final Answer:
1. TRUE
2. TRUE
3. TRUE
4. FALSE
5. TRUE
6. FALSE
7. TRUE
8. FALSE
9. TRUE
10. TRUE
Parent Tip: Review the logic above to help your child master the concept of subsets of real numbers worksheet.
