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 integers, (aRb) means (|a|=|b|). What type of relation is this?On real numbers, (aRb) means (a^2=b^2). What type of relation is this?On non-zero real numbers, (aRb) means (ab>0). What type of relation is this?On real numbers, (aRb) means (a-b>0). Which statement is correct?On real numbers, (aRb) means (a+b=0). Which property is correct?If (A={1,2,3}) and (R={(1,2),(3,3)}), what is the smallest relation needed to make (R) symmetric?If (A={1,2,3}) and (R={(1,1),(2,3)}), which pairs must be added to make (R) reflexive?If (R={(1,2),(2,3)}), which minimum pair must be added to complete transitivity?If (R={(1,2),(2,1),(2,3),(3,2)}), which pair is first required by transitivity?If (R={(1,2),(2,3),(3,4)}), which of the following pairs must be added for a full transitive extension?If a relation (R) has domain ({1,2,3}) and range ({4,5}), what is the domain of (R^{-1})?If (R) is symmetric and transitive but not reflexive, is (R) an equivalence relation?If (R) is an equivalence relation and ((1,2)\in R), ((2,3)\in R), which pair must definitely be in (R)?If (R) is an equivalence relation and ((4,7)\in R), which pair must definitely be in (R)?In the same-parity relation on ({1,2,3,4}), what is the equivalence class of (1)?In ({1,2,3,4,5,6}), how many equivalence classes are formed by the relation of having the same remainder on division by (3)?For the same-remainder modulo (3) relation on ({1,2,3,4,5,6}), what is the equivalence class of (2)?If an equivalence relation gives the partition ({{1,2},{3}}), which pair must be in the relation?For the equivalence relation on (A={1,2,3}) formed by the partition ({{1},{2,3}}), which pair will not be present?How many equivalence relations can be formed on a set with two elements?