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
For the relation R={(1,2),(2,1),(1,1),(2,2)} on A={1,2,3}, which property does R satisfy?If (R={(1,1),(2,2),(3,3),(1,2),(2,2),(2,3)}) on (A={1,2,3}), which pair is required for transitivity?If (R={(1,1),(1,2),(2,1),(2,2)}) on (A={1,2}), what is (R) equal to?If (A={1,2,3}) and (B={x,y,z}), how many relations are possible from (A) to (B)?For R={(1,1),(2,2),(3,3),(2,3),(3,2)} on A={1,2,3}, which property does R fail to satisfy?If (R={(1,1),(2,2),(3,3),(4,4),(1,4),(4,1)}) on (A={1,2,3,4}), is (R) an equivalence relation?If (R={(1,2),(2,3),(3,1)}) on (A={1,2,3}), is (R) symmetric?If (R={(1,2),(2,3),(3,1)}), is (R) transitive?If (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)}) on (A={1,2,3}), is (R) an equivalence relation?On (A={1,2,3,4}), if (aRb) when (a\equiv b \pmod{2}), what is the equivalence class of (1)?On (A={1,2,3,4,5}), if (aRb) when (a\equiv b \pmod{3}), what is the equivalence class of (2)?If in a relation, ((a,b)\in R) and ((b,a)\in R) always imply (a=b), which property is this?On (A={1,2,3}), which properties does the relation (\le) have?If (R={(1,1),(2,2),(3,3),(1,2)}) on (A={1,2,3}), is (R) antisymmetric?If (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), why is (R) not antisymmetric?Which type of relation has reflexivity, antisymmetry and transitivity together?In the divisibility relation on ({1,2,3}), which is the least element?If divisibility relation is defined on (A={2,3,6}), which is the least element?If divisibility relation is defined on (A={1,2,3,6}), which is the greatest element?If (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}) on (A={1,2,3}), is (R) a partial order relation?