Question

Determine whether each set is closed or not closed on the given operation. (3 points)

a. The set of whole numbers on addition
a) Closed
b) Not closed
c) Cannot be determined
d) Depends on specific numbers involved
b. The set of whole numbers on subtraction
a) Closed
b) Not closed
c) Cannot be determined
d) Depends on specific numbers involved
c. The set of even numbers on multiplication
a) Closed
b) Not closed
c) Cannot be determined
d) Depends on specific numbers involved

Answer 1

The set of whole numbers is closed under addition but not under subtraction, while the set of even numbers is closed under multiplication.

Step-by-step explanation:

Determining Closure of Sets with Respect to Operations

To determine whether a set is closed with respect to a given operation, we check if performing the operation on any two elements within the set results in an element that is also in the set.

• a. The set of whole numbers on addition: Closed. When you add any two whole numbers, the result is always another whole number. Therefore, this set is closed with respect to addition.
• b. The set of whole numbers on subtraction: Not closed. Subtracting one whole number from another can result in a negative number, which is not a whole number. Thus, the set of whole numbers is not closed under the operation of subtraction.
• c. The set of even numbers on multiplication: Closed. Multiplying any two even numbers results in another even number, so the set of even numbers is closed under multiplication.