Mathematics
Introduction to Relations
संबंधों का परिचय
In Class 12 Mathematics, under the chapter Relations and Functions, Introduction to Relations explains a relation as a subset of a Cartesian product. Students learn to form and count relations on sets, and identify important examples such as empty, universal and identity relations. The topic also introduces conditions used to recognise reflexive and symmetric relations.
Practice questions
How many equivalence relations can be formed on a set with three elements?Which statement is correct about the empty relation on a non-empty set?Which statement is correct about the universal relation on a non-empty set?If (R) is a reflexive relation on (A), which statement about the domain and range of (R) is correct?If (R) is a symmetric relation on (A), which statement about domain and range is correct?Why is (R={(1,2),(2,1),(2,3),(3,2)}) not transitive?If (R={(1,1),(1,2),(2,2),(2,3),(1,3),(3,3)}) on (A={1,2,3}), which property is correct?If (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}), which missing pair prevents it from being an equivalence relation?On (A={1,2,3}), what is the inverse relation of (R=A\times A)?If (R) is reflexive, will (R^{-1}) also be reflexive?If (R) is symmetric, which statement about (R^{-1}) is correct?If (R={(1,2),(2,3),(1,3),(3,3)}), which pair is required from ((1,3)) and ((3,3)) while checking transitivity?For (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), which is the correct set of equivalence classes?If the relation on (A={1,2,3,4}) is same parity, what is true about ((1,4))?If on (A={1,2,3,4}), (aRb) when (a) and (b) are both even or both odd, which pair belongs to the relation?If (A={1,2,3}) and (R={(1,1),(2,2),(1,2),(2,1)}), what is the domain of (R)?If (A={1,2,3}) and (R={(1,1),(2,2),(1,2),(2,1)}), why is (R) not reflexive?If (R) and (S) are both reflexive relations on (A), what is true about (R\cap S)?If (R) and (S) are both symmetric relations on (A), what is true about (R\cup S)?If (R) and (S) are both transitive relations, which statement about (R\cup S) is correct?