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
In the divisibility relation on (A={2,4,6,12,18}), how many minimal elements are there?In the divisibility relation on (A={1,2,3,6}), how many comparable unordered pairs ({a,b}) with (a\ne b) are there?In the divisibility relation on (A={1,2,3,6}), how many elements can a longest chain contain?In the divisibility relation on (A={1,2,4,8,16}), what is the least upper bound of (2) and (8)?In the divisibility relation on (A={1,2,4,8,16}), what is the greatest lower bound of (4) and (16)?If (R) is reflexive and transitive on a set, which statement about (R\circ R) is always true?On (A={1,2,3,4}), for (R={(1,2),(2,3),(3,4)}), what is (R\circ R)?On (A={1,2,3,4}), for (R={(1,2),(2,3),(3,4)}), what is (R\circ R\circ R)?On (A={1,2,3}), for (R={(1,2),(2,1),(2,3),(3,2)}), which pair will not belong to (R\circ R)?If (R) is a symmetric relation, which statement about (R\circ R^{-1}) is correct?For any relation (R), what is ((R^{-1})^{-1}) equal to?If (R) and (S) are relations, what is ((R\cup S)^{-1}) equal to?If (R) and (S) are relations, what is ((R\cap S)^{-1}) equal to?If (R\subseteq S), which statement about inverse relations is correct?If (R) is transitive, which statement about (R^3\subseteq R) is correct?On (A={1,2,3,4}), for (R={(1,2),(2,1),(2,3),(3,4)}), which pair must be added to make it transitive?On (A={1,2,3,4}), which pair will belong to the transitive closure of (R={(1,2),(2,1),(2,3),(3,4)})?Which pair must belong to the smallest equivalence relation on A={1,2,3,4} containing R={(1,2),(2,3),(4,4)}?On (A={1,2,3,4,5}), how many pairs are in the smallest equivalence relation containing (R={(1,2),(2,3),(4,5)})?Which pair is not present in the smallest equivalence relation on A={1,2,3,4} containing R={(1,2),(2,3),(3,1)}?