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) and (S) are both symmetric relations, which statement about (R-S) is correct?If (R) and (S) are both reflexive relations, which statement about (R-S) is correct?If (R) is a symmetric relation, which statement about (R\cup R^{-1}) is correct?For any relation (R), what is (R\cap R^{-1}) always like?For any relation (R), which property does (R\cup R^{-1}) always have?If (R) is a reflexive relation on (A), which statement about (R\circ R) is always true?If (R) is a transitive relation, which statement about (R\circ R) is always true?On (A={1,2,3}), (R={(1,2),(2,3)}). What is (R\circ R)?On (A={1,2,3}), (R={(1,2),(2,1),(2,3)}). Which pair must belong to (R\circ R)?On (A={1,2,3}), (R={(1,1),(1,2),(2,3),(3,3)}). Why is this relation not transitive?If (A) has (5) elements, how many antisymmetric relations can be formed on (A)?If (A) has (4) elements, how many symmetric and irreflexive but non-empty relations are there on (A)?What is the greatest possible number of pairs in a relation on A={1,2,3,4} that is both symmetric and antisymmetric?If (A) has (5) elements, how many relations are reflexive, symmetric and antisymmetric all together?If (A) has (5) elements, what is the total number of equivalence relations on (A)?On (A={1,2,3,4,5}), how many equivalence relations have exactly two equivalence classes?On (A={1,2,3,4,5,6}), how many equivalence relations have two classes both of size (3)?On (A={1,2,3,4,5,6}), how many equivalence relations have class sizes (2,2,2)?If (A={1,2,3,4,5}), how many equivalence relations have (1,2,3) in the same class?If (A={1,2,3,4,5}), how many equivalence relations have (1) and (2) in the same class but (3) not in that class?