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Subjects
Class 12MathematicsRelations and FunctionsSymmetric relationHard
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If (M) is the matrix of a relation (R), what is the correct matrix condition for (R) to be symmetric?

Answer and explanation

Correct answer: (M=M^T)

Step 1: ((a_i,a_j)) in a relation means (m_{ij}=1). Step 2: Symmetry requires ((a_j,a_i)), meaning (m_{ji}=1). Step 3: Thus (m_{ij}=m_{ji}) for all (i,j), so (M=M^T).

Related tags

Relation MatrixTransposeSymmetric RelationRelations And FunctionsMathematicsClass 12 Mcq
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10 more MCQs
  1. 1Let A={1,2,3}. If a symmetric relation R on A must contain (1,2), how many such relations are possible?
  2. 2On A={1,2}, which property is satisfied by R={(1,1),(1,2),(2,1)}?
  3. 3If A has n elements, what is the number of symmetric relations on A?
  4. 4Which relation on A={1,2,3} is symmetric but not transitive?
  5. 5For a five-element set A, how many symmetric relations on A contain no diagonal ordered pair (a,a)?
  6. 6On the set (A={1,2,3}), the relation (R={(1,2),(2,1),(3,3)}) is given. What type of relation is it?
  7. 7If a relation (R) contains ((4,7)) and (R) is symmetric, which ordered pair must definitely be in (R)?
  8. 8On (A={1,2}), (R={(1,1),(1,2)}) is given. Which pair must be added to make it symmetric?
  9. 9Which statement correctly identifies a symmetric relation?
  10. 10On the set (A={1,2,3}), which relation is not symmetric?
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