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Concept explainers
(a)
Is the set of whole numbers closed under subtraction . If not give a counterexample.
Given :
If you take any two whole numbers and add them together, the sum is always a whole number. This is the closure property for addition. The set of whole number is cosed under addition.
Explanation:
In order to find is the set of whole numbers closed under subtraction . If not give a counterexample, No the set of whole numbers is not closed under subtraction . for example:
Which is not a whole number.
(b)
Would this set be closed under addition. If not give a counterexample.
NO
Given :
If you take any two whole numbers and add them together, the sum is always a whole number. This is the closure property for addition. The set of whole number is cosed under addition. Suppose you had a very small set of numbers that contained only 0 and 1.
Explanation:
In order to find would this set be closed under addition. If not give a counterexample, No this set would not be closed under addition because for example:
Which is outside the set .
(c)
There is also a closure property for multiplication of whole numbers. State this property using the addition property above as a guideline.
Given :
If you take any two whole numbers and add them together, the sum is always a whole number. This is the closure property for addition. The set of whole number is cosed under addition. There is also a closure property for multiplication of whole numbers.
Explanation:
In order to write the property using the addition property, there is also a closure property for multiplication of whole numbers, now to state this property using the addition property, if you take any two whole numbers and multiply them, the product is always a whole number.
(d)
Is the set (0,1) closed under multiplication. Explain.
Explanation:
In order to find the set (0,1) is closed under multiplication, first closed under multiplication means if you take any two whole number and multiply them, the product is always a whole number, so multiplying 0 and 1 then it will get 0 which is a whole number.
So, the set (0,1) is closed under multiplication.
Chapter 1 Solutions
Glencoe Math Accelerated, Student Edition
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