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+b) is odd(}). What type of relation is it?On (A={1,2,3,4,5,6}), (aRb) iff (a) and (b) leave the same remainder on division by (2). How many equivalence classes are formed?On (A={1,2,3,4,5}), (aRb) iff (a\equiv b\pmod 3). How many equivalence classes are formed?On (A={1,2,3,4,5}), (R={(a,b):a+b\equiv0\pmod 3}). Which property does this relation satisfy?On (A={1,2,3,4}), how many pairs are in (R={(a,b):a-b\equiv0\pmod2})?On (A={1,2,3,4,5}), how many pairs are in (R={(a,b):a+b\le6})?On (A={1,2,3,4,5}), how many pairs are in (R={(a,b):a<b})?On (A={1,2,3,4,5}), how many pairs are in (R={(a,b):a\le b})?In the divisibility relation on (A={1,2,3,4,6,12}), how many pairs are there?In the divisibility relation on (A={1,2,3,4,6,12}), what is the least upper bound of (3) and (4)?In the divisibility relation on (A={1,2,3,4,6,12}), what is the greatest lower bound of (4) and (6)?In the divisibility relation on (A={2,3,6,9,18}), does a least element exist?In the divisibility relation on (A={2,3,6,9,18}), which is the greatest element?In the divisibility relation on (A={2,4,8,16}), how many elements are in the longest chain of the Hasse diagram?In the divisibility relation on (A={2,3,6,12}), which two elements are not comparable?On (A={1,2,3}), how many pairs are in the smallest equivalence relation containing (R={(1,2),(2,1)})?On (A={1,2,3,4}), how many pairs are in the smallest equivalence relation containing (R={(1,2),(2,3)})?On (A={1,2,3,4}), which new pair is minimally needed to make (R={(1,2),(2,3),(4,4)}) transitive?On (A={1,2,3}), what is the transitive closure of (R={(1,2),(2,1)})?On (A={1,2,3,4}), how many pairs are in the transitive closure of (R={(1,2),(2,3),(3,4)})?