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
Which can be the most direct reason for a relation not being an equivalence relation?Why is (R={(1,1),(2,2),(3,3),(1,2)}) not an equivalence relation on (A={1,2,3})?If (R) is reflexive and symmetric but not transitive, what can be said about (R)?Which property is clearly present in (R={(1,1),(2,2),(3,3),(1,3),(3,1)})?If (R={(1,1),(1,2),(2,2)}), which pair is needed for transitivity from ((1,2)) and ((2,2))?If (R={(1,1),(1,2),(2,2)}) on (A={1,2}), is it transitive?If (R={(1,2),(2,1)}) on (A={1,2}), why is it not reflexive?On (A={1,2,3}), which property is definitely held by (R={(1,1),(2,2),(3,3)})?Why is (R={(1,1),(2,2),(3,3)}) symmetric on (A={1,2,3})?Why is (R={(1,1),(2,2),(3,3)}) transitive on (A={1,2,3})?If a relation has domain ({1,2}) and range ({3,4}), which pair may be possible?If (R={(1,2),(2,4),(3,6),(4,8)}), what is the domain?If (R={(1,2),(2,4),(3,6),(4,8)}), what is the range?If (A={1,2,3}) and (R={(1,2),(2,3)}), is (R) a relation on (A)?If (A={1,2}), which pair is not in (A\times A)?If (R={(2,2),(4,4),(6,6),(2,4),(4,2)}) on (A={2,4,6}), which property is immediately visible?Which property does not fail in (R={(1,2),(2,1),(1,1),(2,2)})?If (R={(1,1),(1,2),(2,2),(2,3),(1,3)}), which pair completes transitivity because of ((1,2)) and ((2,3))?If a relation contains ((5,7)) and is symmetric, which pair must be present?If a relation contains ((2,5)) and ((5,9)), and the relation is transitive, which pair must be present?