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 relation contains only self-pairs, what is it commonly called?Which relation is the empty relation on (A={1,2})?Which relation is the universal relation on (A={1,2})?If (R={(1,1),(2,2),(1,2),(2,1)}), is it an equivalence relation on (A={1,2})?If (R={(1,1),(2,2),(1,2)}), why is it not an equivalence relation?If (A={1,2,3}) and (R=A\times A), what type of relation is (R)?If (R\subseteq A\times A), what can (R) be called?Which pair will be in the identity relation on (A={2,4})?If (A) has (5) elements, how many pairs are there in (A\times A)?In which relation is every element related to itself and no element is left out?If (A) has (3) elements and (B) has (2) elements, what is the total number of relations from (A) to (B)?If (A) has (3) elements, what is the number of reflexive relations on (A)?If (A) has (3) elements, what is the number of symmetric relations on (A)?If (A) has (3) elements, what is the number of relations on (A) that are both reflexive and symmetric?On integers, (aRb) means (a-b) is even. What type of relation is this?On natural numbers, (aRb) means (a\le b). Which statement is correct?On natural numbers, (aRb) means (a<b). Which property is correct?On natural numbers, (aRb) means (a\mid b). Which statement is correct?On integers, (aRb) means (a+b) is even. What type of relation is this?On integers, (aRb) means (a-b) is divisible by (3). What type of relation is this?