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 (R={(1,2),(2,4),(4,1)}), what is (R^{-1})?If (R={(1,2),(2,3)}) and (S={(2,4),(3,5)}), what is (S\circ R)?If (R={(1,2),(2,1),(2,3)}), which pair must be in (R\circ R)?If (R={(1,2),(2,1),(2,3),(3,2)}) on (A={1,2,3}), why is (R) symmetric but not an equivalence relation?If a relation on (A={1,2,3}) is reflexive, symmetric and antisymmetric all together, how many pairs will it have?If a relation on (A={1,2,3,4}) is reflexive, symmetric and antisymmetric all together, which relation will it be?If (R) is the universal relation on a non-empty set (A), which statement is always true?If the universal relation is on (A={1,2}), is it antisymmetric?If the universal relation is on (A={1}), which statement is correct?If (R={(1,1),(2,2),(3,3),(1,2),(2,3),(3,1)}) on (A={1,2,3}), why is (R) not transitive?If (R={(1,2),(2,3),(3,1),(1,1),(2,2),(3,3),(1,3),(2,1),(3,2)}) on (A={1,2,3}), what is (R)?If equivalence classes of (R) on (A={1,2,3,4}) are ({1,4}), ({2}), and ({3}), how many pairs are in (R)?If the only equivalence class of (R) on (A={1,2,3,4}) is ({1,2,3,4}), how many pairs are in (R)?If all equivalence classes of (R) on (A={1,2,3,4}) are singletons, how many pairs are in (R)?If (R) on (A={1,2,3}) is reflexive and symmetric and ((1,2)) and ((2,3)) are in (R), which pairs must be present to make it an equivalence relation?On (A={1,2,3,4}), if (aRb) when (a+b=5), how many pairs are in (R)?On (A={1,2,3,4}), if (aRb) when (a+b=5), which statement is correct?On (A={1,2,3}), if (aRb) when (|a-b|\le1), how many pairs are in (R)?On (A={1,2,3}), if (aRb) when (|a-b|\le1), which property is absent?On (A={1,2,3,4}), if (aRb) when (|a-b|) is even, how many pairs are in (R)?