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Which of the following statement is false?
a) Integers are closed under addition
b) Integers are closed under subtraction
c)Integers are closed under multiplication
d) Integers are closed under division?
a) Integers are closed under addition
b) Integers are closed under subtraction
c)Integers are closed under multiplication
d) Integers are closed under division?
Most Upvoted Answer
Which of the following statement is false?a) Integers are closed under...
Understanding Closure Property of Integers
The closure property refers to whether performing a specific operation on elements within a set results in an element that is also within the same set. Let's evaluate the statements regarding integers:
Closure Under Addition
- Integers are closed under addition.
- Adding any two integers results in another integer (e.g., 2 + 3 = 5).
Closure Under Subtraction
- Integers are closed under subtraction.
- Subtracting one integer from another also yields an integer (e.g., 5 - 3 = 2).
Closure Under Multiplication
- Integers are closed under multiplication.
- Multiplying any two integers results in another integer (e.g., 4 x 2 = 8).
Closure Under Division
- Integers are NOT closed under division.
- Dividing one integer by another may result in a non-integer (e.g., 1 ÷ 2 = 0.5, which is not an integer).
Conclusion
The false statement among the options provided is:
- d) Integers are closed under division.
In summary, while integers are closed under addition, subtraction, and multiplication, they do not maintain closure under division as the result can be a non-integer. Understanding these properties is crucial in mathematics, especially in higher-level studies such as those tested in UPSC.
The closure property refers to whether performing a specific operation on elements within a set results in an element that is also within the same set. Let's evaluate the statements regarding integers:
Closure Under Addition
- Integers are closed under addition.
- Adding any two integers results in another integer (e.g., 2 + 3 = 5).
Closure Under Subtraction
- Integers are closed under subtraction.
- Subtracting one integer from another also yields an integer (e.g., 5 - 3 = 2).
Closure Under Multiplication
- Integers are closed under multiplication.
- Multiplying any two integers results in another integer (e.g., 4 x 2 = 8).
Closure Under Division
- Integers are NOT closed under division.
- Dividing one integer by another may result in a non-integer (e.g., 1 ÷ 2 = 0.5, which is not an integer).
Conclusion
The false statement among the options provided is:
- d) Integers are closed under division.
In summary, while integers are closed under addition, subtraction, and multiplication, they do not maintain closure under division as the result can be a non-integer. Understanding these properties is crucial in mathematics, especially in higher-level studies such as those tested in UPSC.
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Which of the following statement is false?a) Integers are closed under addition b) Integers are closed under subtraction c)Integers are closed under multiplication d) Integers are closed under division?
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Which of the following statement is false?a) Integers are closed under addition b) Integers are closed under subtraction c)Integers are closed under multiplication d) Integers are closed under division? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Which of the following statement is false?a) Integers are closed under addition b) Integers are closed under subtraction c)Integers are closed under multiplication d) Integers are closed under division? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statement is false?a) Integers are closed under addition b) Integers are closed under subtraction c)Integers are closed under multiplication d) Integers are closed under division?.
Which of the following statement is false?a) Integers are closed under addition b) Integers are closed under subtraction c)Integers are closed under multiplication d) Integers are closed under division? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Which of the following statement is false?a) Integers are closed under addition b) Integers are closed under subtraction c)Integers are closed under multiplication d) Integers are closed under division? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statement is false?a) Integers are closed under addition b) Integers are closed under subtraction c)Integers are closed under multiplication d) Integers are closed under division?.
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