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With respect to which of the following operations is closure property satisfied by the set of integers?
- a)+,×
- b)+,÷,×
- c)+,×,−
- d)+,−,÷
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
With respect to which of the following operations is closure property ...
The closure property states that when you perform an operation on any two numbers in a set, the result of the computation is another number in the same set .Since division can result in changing an integer in decimals. So its closed in addition, subtraction and multplication.
Most Upvoted Answer
With respect to which of the following operations is closure property ...
Addition (+)
b) Subtraction (-)
c) Multiplication (*)
d) Division (/)
a) Addition (+) satisfies closure property for the set of integers.
Explanation:
Closure property means that the result of an operation on any two elements of the set is also an element of the same set.
For addition of integers, if we take any two integers a and b, their sum a+b is also an integer. Therefore, the set of integers satisfies closure property for addition.
However, subtraction, multiplication, and division do not satisfy closure property for all pairs of integers. For example, if we subtract 5 from 3, the result (-2) is not an integer. Similarly, if we divide 4 by 5, the result (0.8) is not an integer. Therefore, options b, c, and d do not satisfy closure property for the set of integers.
b) Subtraction (-)
c) Multiplication (*)
d) Division (/)
a) Addition (+) satisfies closure property for the set of integers.
Explanation:
Closure property means that the result of an operation on any two elements of the set is also an element of the same set.
For addition of integers, if we take any two integers a and b, their sum a+b is also an integer. Therefore, the set of integers satisfies closure property for addition.
However, subtraction, multiplication, and division do not satisfy closure property for all pairs of integers. For example, if we subtract 5 from 3, the result (-2) is not an integer. Similarly, if we divide 4 by 5, the result (0.8) is not an integer. Therefore, options b, c, and d do not satisfy closure property for the set of integers.
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Community Answer
With respect to which of the following operations is closure property ...
Add, subtract, multiply - you'll get an integer. Divide? Sometimes you might get a fraction which is not an integer.
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With respect to which of the following operations is closure property satisfied by the set of integers?a)+,× b)+,÷,×c)+,×,− d)+,−,÷Correct answer is option 'C'. Can you explain this answer?
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