Let’s go through each question one at a time, step by step.
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Question 1:
> The counting numbers starting from 1 and going to infinity belong to the set of ___.
Counting numbers are: 1, 2, 3, 4, 5, ... and so on forever.
These are also called
Natural Numbers, and they’re usually labeled with the letter
N.
Whole numbers include 0 too — so that’s not right here.
Integers include negative numbers — nope.
Rational numbers include fractions — way too broad.
✔ So the correct answer is:
Natural numbers, N
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Question 2:
> The symbol ⊂ means "is a subset of". Which of the following is true for the set of rational numbers, Q, the set of whole numbers, W, and the set of integers, Z?
First, let’s remember what these sets mean:
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W (Whole numbers): 0, 1, 2, 3, ...
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Z (Integers): ..., -3, -2, -1, 0, 1, 2, 3, ...
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Q (Rational numbers): Any number that can be written as a fraction (like 1/2, -4/7, 5, etc.)
Now, “subset” means all elements of one set are inside another set.
Is Q ⊂ W? No — because Q includes fractions like 1/2, which aren’t in W.
Is Q ⊂ Z? No — same reason. Fractions aren’t integers.
Is W ⊂ Q? YES! Every whole number (0, 1, 2, 3...) can be written as a fraction (like 0/1, 1/1, 2/1...). So W is inside Q.
Is Z ⊂ W? No — because Z has negative numbers, and W doesn’t.
✔ So the correct answer is:
W ⊂ Q
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Question 3:
> Which two sets when combined make up all of the real numbers?
Real numbers = everything you can think of on the number line.
They split into two big groups:
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Rational numbers (can be written as fractions)
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Irrational numbers (cannot be written as fractions — like √2 or π)
Together, those two cover EVERY real number.
Other options don’t work:
- Integers + whole numbers → still missing fractions and irrationals.
- Irrationals + integers → missing non-integer rationals like 1/2.
- Rationals + naturals → naturals are already part of rationals, and we’re still missing irrationals.
✔ So the correct answer is:
Rational numbers and irrational numbers
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Final Answer:
1. Natural numbers, N
2. W ⊂ Q
3. Rational numbers and irrational numbers
Parent Tip: Review the logic above to help your child master the concept of subsets of real numbers worksheet.
