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}), (R={(a,b):a\le b}). How many ordered pairs are in the relation?On (A={1,2,3,4,5}), (R={(a,b):a+b) is even(}). How many ordered pairs are in the relation?On (A={1,2,3,4,6,12}), (R={(a,b):a) divides (b)(}). Which statement about ((3,12)) and ((12,3)) is correct?If (R) is an equivalence relation and (aRb), what is true about ([a]) and ([b])?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}). Why is it not an equivalence relation?How many ordered pairs are in the identity relation on (A={1,2,3,4})?If (A={1,2,3}) and (B={4,5}), what is the total number of relations from (A) to (B)?On (A={1,2,3}), relation (R=A\times A). Which relation is it?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(1,3)}). Is this relation antisymmetric?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1)}). What are the equivalence classes?If (A) has (3) elements, how many relations on (A) are both reflexive and symmetric?If (A) has (3) elements, how many relations on (A) are both symmetric and antisymmetric?If (A) has (3) elements, what is the number of reflexive and antisymmetric relations on (A)?For (R={(1,1),(2,2),(3,3),(1,2),(2,3)}) on (A={1,2,3}), which minimum pair must be added to make it transitive?If (R={(1,2),(2,3),(3,4)}), which additional pairs must appear in the transitive closure?What is the smallest change needed to make R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)} an equivalence relation on A={1,2,3}?For the partition ({{1,4},{2,3}}) of (A={1,2,3,4}), how many pairs are in the equivalence relation formed by it?For the partition ({{1,2,3},{4}}) of (A={1,2,3,4}), how many pairs are in the equivalence relation formed by it?If (aRb) on (A={1,2,3,4,5,6}) when (a\equiv b \pmod{3}), what is the equivalence class of (1)?If (aRb) on (A={1,2,3,4,5,6,7}) when (a-b) is divisible by (4), what is the equivalence class of (3)?