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
On (A={1,2,3,4}), if (aRb) when (a+b=5), why is (R) not transitive?If (R={(1,1),(2,2),(1,2),(2,1),(3,3)}) on (A={1,2,3}), what are the equivalence classes formed by (R)?If the classes of (R) on (A={1,2,3,4}) are ({1,2}) and ({3,4}), which pair will not be in (R)?If (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}) on (A={1,2,3}), which pairs must be added to make it an equivalence relation?If (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}) on (A={1,2,3}), which pair will be in (R^{-1}) but not in (R)?If (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}) on (A={1,2,3}), which description fits (R) best?If (R={(1,2),(2,1),(2,3),(3,2),(1,3),(3,1)}) on (A={1,2,3}), why is (R) symmetric but not reflexive?If (R={(1,2),(2,3),(1,3)}) on (A={1,2,3}), is (R) transitive?If (R={(1,2),(2,3),(3,1)}) on (A={1,2,3}), why is (R) not transitive?If a relation (R) on (A={1,2,3,4}) forms two classes ({1,3}) and ({2,4}), how many pairs will be in (R)?If a relation (R) on (A={1,2,3,4}) puts all elements in one equivalence class, what relation is (R)?If all equivalence classes of (R) on (A={1,2,3,4}) are singletons, what relation is (R)?If (R) on (A={1,2,3}) is reflexive and symmetric and ((1,2),(2,3)\in R), which pair is necessary to make (R) an equivalence relation?If (R) is a partial order relation on (A={1,2,3}) and ((1,2),(2,1)\in R), what conclusion follows?If (R) is reflexive and transitive, what decides whether (R) is symmetric?If (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3),(3,1)}) on (A={1,2,3}), which property definitely fails?If (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3)}) on (A={1,2,3}), which pair is missing for symmetry?If (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4),(1,4)}) on (A={1,2,3,4}), what type of relation is (R)?If (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4)}) on (A={1,2,3,4}), why is (R) not a partial order relation?If a relation on (A={1,2,3}) is reflexive, symmetric and antisymmetric all together, which relation can it be?