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}), (R={(1,2),(2,3),(1,3)}). What is (R^{-1})?On (A={1,2,3,4}), (R={(a,b):a\mid b}). Why is this relation a partial order?In (R={(a,b):a\le b}) on (A={1,2,3,4}), which is the least element?In the divisibility relation on (A={2,3,6,12}), which is the greatest element?In the divisibility relation on (A={2,3,4,6,12}), what is the least upper bound of (2) and (3)?In the divisibility relation on (A={1,2,3,6,12}), what is the greatest lower bound of (6) and (12)?In the divisibility relation on (A={2,3,5,30}), how many minimal elements are there?In the divisibility relation on (A={2,3,5,30}), how many maximal elements are there?On (A={1,2,3}), how many relations are neither reflexive nor irreflexive?If (A) has (n) elements, what is the number of irreflexive relations on (A)?If (A) has (n) elements, what is the number of relations on (A) that are both symmetric and irreflexive?If (A) has (4) elements, how many relations on (A) are both irreflexive and antisymmetric?On (A={1,2,3}), how many relations contain exactly two diagonal pairs?On (A={1,2,3,4}), how many symmetric relations contain exactly two diagonal pairs?On (A={1,2,3}), how many reflexive relations are not symmetric?On (A={1,2,3}), how many symmetric relations are not reflexive?On (A={1,2,3}), how many relations are both symmetric and antisymmetric but not reflexive?On (A={1,2,3,4}), (R={(a,b):a+b\le 5}). How many pairs are in (R)?On (A={1,2,3,4,5}), (R={(a,b):a+b) is divisible by (3)(}). How many pairs are in (R)?On (A={1,2,3,4,5,6}), (R={(a,b):\gcd(a,b)=1}). Which property does this relation satisfy?