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 (A) has (n) elements, which formula gives the total number of relations on (A)?If (A) has (n) elements, which formula gives the number of reflexive relations on (A)?If (A) has (n) elements, which formula gives the number of symmetric relations on (A)?If (A) has (n) elements, which formula gives the number of relations that are both reflexive and symmetric on (A)?On (A={1,2,3}), (R={(1,1),(2,2),(1,2),(2,3),(1,3)}). Which property does this relation satisfy?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}). What is the main reason it is not an equivalence relation?If a relation always contains ((a,c)) whenever it contains ((a,b)) and ((b,c)), which property does it have?On (A={1,2,3,4}), (R={(a,b): |a-b|) is even(}). How many equivalence classes are formed?On (A={1,2,3,4,5,6}), (aRb) iff (a) and (b) leave the same remainder on division by (3). What is the class of (2)?On (A={1,2,3,4}), (R={(a,b):a-b) is odd(}). What type of relation is it?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2)}). What type of relation is it?If (R) and (S) are reflexive relations on (A), which statement about (R\cap S) is correct?If (R) and (S) are symmetric relations on (A), which statement about (R\cup S) is correct?If (R) and (S) are transitive relations on (A), which statement about (R\cup S) is correct?For (R={(1,2),(2,3)}) on (A={1,2,3}), which minimum pair must be added to make it transitive?For (R={(1,2)}) on (A={1,2,3}), which minimum pair must be added to make it symmetric?For (R={(1,2),(2,1)}) on (A={1,2,3}), how many minimum pairs must be added to make it reflexive?On (A={1,2,3,4}), (R={(a,b):a+b=5}). Which property does this relation satisfy?On real numbers, (aRb) iff (a-b>0). What type of relation is it?On (A={1,2,3,4}), (R={(a,b):a) and (b) are both even or both odd(}). What type of relation is it?