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 real numbers, (aRb) iff (a-b) is an integer. What type of relation is it?On real numbers, (aRb) iff (a-b) is irrational. Which statement is correct?On real numbers, (aRb) iff (a^3=b^3). What type of relation is it?On real numbers, (aRb) iff (a^2\le b^2). Which statement is correct?On real numbers, (aRb) iff (|a|=|b|). What type of relation is it?On real numbers, (aRb) iff (a^2+b^2=0). What type of relation is it?For a non-empty set (A), which statement about the empty relation is correct?On (A={1,2,3}), (R={(1,2),(2,3),(1,3)}). What type of relation is it?On (A={1,2,3,4}), (R={(1,2),(2,4),(1,4),(3,3)}). Which property does this relation satisfy?On (A={1,2,3}), (R={(1,2),(2,1),(1,1)}). Which minimum pair must be added for transitivity?For (R={(1,2),(2,3),(3,4)}) on (A={1,2,3,4}), how many minimum pairs must be added to form the transitive closure?On (A={1,2,3}), starting from (R={(1,2),(2,3)}), how many pairs will the smallest relation containing (R) and being reflexive, symmetric and transitive have?On (A={1,2,3,4}), how many pairs are in the smallest equivalence relation containing (R={(1,2),(3,4)})?If (R) and (S) are equivalence relations on (A), which statement about (R\cap S) is correct?Is the union of two equivalence relations always an equivalence relation?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) and (S={(1,1),(2,2),(3,3),(2,3),(3,2)}). Why is (R\cup S) not an equivalence relation?If (R) is a relation on a set (A), when will (R^{-1}) be symmetric?If (R) is a reflexive relation, which statement about (R^{-1}) is correct?If (R) is an equivalence relation, which statement about (R^{-1}) is correct?If a relation (R) is transitive, which statement about (R^{-1}) is correct?