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Subjects

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

If (A={1,2,3}) and (R={(1,1),(2,2),(3,3),(1,2),(2,1)}), what type of relation is (R)?If (R={(1,1),(2,2),(3,3),(1,2),(2,3)}) on (A={1,2,3}), why is (R) not an equivalence relation?If a set (A) has (4) elements, how many relations are possible on (A)?For a set A with 3 elements, how many relations are not reflexive?If (R={(1,1),(2,2),(3,3),(1,2)}), why is (R) not symmetric on (A={1,2,3})?If (R={(1,2),(2,3)}), which pair must be added to make it transitive?If (A={1,2,3}), which is the identity relation on (A)?If (A) has (2) elements and (B) has (3) elements, how many relations are possible from (A) to (B)?If (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) on (A={1,2,3}), which properties are definite?If (R={(1,2),(2,1),(2,3),(3,2)}), why is it not reflexive on (A={1,2,3})?Choose the correct statement for (R={(1,1),(1,2),(2,2),(2,3),(1,3),(3,3)}) on (A={1,2,3}).If (R={(1,1),(2,2),(3,3),(1,3)}) on (A={1,2,3}), which property is definitely absent?If (A={1,2,3}), how many ordered pairs are in the universal relation on (A)?In which relation is every element related to itself, but the reverse-pair condition is not necessary?If (R) is a relation on (A) such that ((a,b)\in R\Rightarrow (b,a)\in R), what type of relation is (R)?If (R) is a relation on (A) such that ((a,b)\in R) and ((b,c)\in R\Rightarrow (a,c)\in R), what type of relation is (R)?If (R) contains all pairs of (A\times A) on (A={1,2,3}), what is (R)?If (R=\varnothing) on (A={1,2,3}), which statement about (R) is correct?If A has 3 elements, how many symmetric relations on A are also reflexive?If (R={(1,1),(2,2),(1,2),(2,1)}) on (A={1,2}), what is (R)?