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Subjects
Class 12MathematicsRelations and FunctionsBinary operationsMedium
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On the set (A={1,2,3,4,5}), the operation (a*b=\max(a,b)) is defined. Which element is the identity element?

Answer and explanation

Correct answer: (1)

Step 1: For identity (e), (\max(a,e)=a) must hold for all (a \in A). Step 2: This is possible only when (e) is the least element of (A). Step 3: In a maximum operation, the least element is the identity.

Related tags

Binary OperationsMaximum OperationIdentityRelations 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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