Closure Property of Real Number Addition and Multiplication
Definition of Closure Property of Real Number Addition and Multiplication

Closure property of real number addition states that the sum of any two real numbers equals another real number.

Closure property of real number multiplication states that the product of any two real numbers equals another real number.
Examples of Closure Property of Real Number Addition and Multiplication
2 + 5 = 7, another real number.
4 × 7 = 28, another real number.
Solved Example on Closure Property of Real Number Addition
Determine the set that does not satisfy closure property of addition.
Choices:
A. Real number
B. Irrational numbers
C. Rational numbers
D. Integers
Correct Answer: B
Solution:
Step 1: Among the sets listed, only the set of irrational numbers does not satisfy closure property of addition.
Step 2: For example, consider the irrational numbers
and
.
Step 3: is a rational number.
Step 4: So, the set of irrational numbers does not satisfy the Closure property under addition.
Solved Example on Closure Property of Real Number Multiplication
Determine whether the set {0, 11,  11} satisfies closure property with respective to multiplication.
Choices:
A. Yes
B. No
Correct Answer: B
Solution:
Step 1:
{0, 11,  11}
Step 2:
0 × 11 = 0 [0 is an element of the set.]
Step 3:  11 × 0 = 0 [0 is an element of the set.]
Step 4:  11 × 11 =  121, not an element of the given set.
Step 5: So, the given set does not satisfy the closure property with respective to multiplication.
Related Terms for Closure Property of Real Number Addition and Multiplication
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