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Class 12MathematicsRelations and FunctionsBinary operationsEasy
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On the set of natural numbers (N), the operation (a\ast b=a-b) is given. Is it a binary operation on (N)?

Answer and explanation

Correct answer: No, because the result may not be a natural number

Step 1: For a binary operation on (N), (a-b) must always be in (N). Step 2: (2-5=-3), which is not in (N). Step 3: One counterexample is enough to reject closure.

Related tags

Binary OperationNatural NumbersClosureBinary OperationsRelations And FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  1. 1What is the correct meaning of a binary operation on a set (A)?
  2. 2If (a,b\in A) implies (a*b\in A), which property does this show?
  3. 3Why is usual addition (+) a binary operation on the set of natural numbers (\mathbb{N})?
  4. 4Why is usual subtraction (-) not a binary operation on the set of natural numbers (\mathbb{N})?
  5. 5How is usual multiplication (\times) on the set of integers (\mathbb{Z})?
  6. 6Why is usual division (\div) not a binary operation on the set of integers (\mathbb{Z})?
  7. 7If (a*b=a+b) is defined on real numbers, what type of operation is it?
  8. 8If (a*b=a-b) is defined on real numbers, which statement is correct?
  9. 9On real numbers, (a*b=a+b+1). What is the identity element of this operation?
  10. 10On real numbers, (a*b=a+b+ab). Which is the identity element of this operation?
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