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={1,2,3}), how many total relations can be formed from (A) to (A)?If (A) has (4) elements, what is the number of reflexive relations on (A)?How many symmetric relations are there on (A={1,2,3})?How many relations on (A={1,2,3}) are both reflexive and symmetric?On the set of integers, relation (R) is defined by (aRb) if (a-b) is divisible by (5). What type of relation is it?For real numbers, relation (R) is defined by (aRb) iff (a\le b). Which statement is correct?On (A={1,2,3,4}), relation (R={(a,b):a) divides (b)(}). What type of relation is it?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,1)}). What type of relation is it?On (A={1,2,3}), (R={(1,1),(2,2),(3,3),(1,2),(2,3)}). Which property is missing?If a relation is both symmetric and antisymmetric, what is true about its off-diagonal pairs?Which is the smallest reflexive relation on (A={1,2,3})?Which statement is always true for the universal relation on a set (A)?On which set can the empty relation be considered reflexive?If (R) is an equivalence relation on (A), which statement about its equivalence classes is correct?On integers, (aRb) iff (a) and (b) leave the same remainder when divided by (4). What is the equivalence class of (0)?On (A={1,2,3,4}), (R={(a,b):a+b) is even(}). What type of relation is it?On real numbers, (aRb) iff (a-b) is rational. What type of relation is it?On real numbers, (aRb) iff (a^2=b^2). What type of relation is it?On real numbers, (aRb) iff (a<b). Which statement is correct?On (A={1,2,3}), (R={(1,2),(2,1),(2,3),(3,2)}). Which property does this relation satisfy?