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 (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), which conclusion is correct?Choose the correct statement for (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}) on (A={1,2,3}).If (R={(1,1),(2,2),(3,3)}) on (A={1,2,3}), which statement about (R) is correct?In which situation will a relation (R) on (A) not be reflexive?If (A={1,2,3,4}), what is the number of reflexive relations on (A)?If (A={1,2}) and (B={3,4}), which can be a relation from (A) to (B)?If (R={(1,2),(2,1)}), what must be added to make it reflexive on (A={1,2})?If (R={(1,2),(2,3),(3,1)}), which pairs must be added to make (R) symmetric?If (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) on (A={1,2,3}), which pairs are still needed for equivalence?On (A={1,2,3}), if (aRb) when (a=b), which relation does (R) represent?On (A={1,2,3}), if (aRb) when (a\le b), what type of relation is it?On (A={1,2,3}), if (aRb) when (a<b), which statement is correct?On (A={1,2,3,4}), if (aRb) when (a-b) is even, what type of relation is (R)?On the set of integers, (aRb) if (a-b) is divisible by (3). What type of relation is this?If (R={(1,2),(2,3),(3,3)}), what is (R^{-1})?Under which condition is (R^{-1}=R)?If (R={(1,1),(2,2),(3,3),(1,2),(1,3)}) on (A={1,2,3}), which property is definitely present?If (R={(1,2),(2,1),(2,3),(3,2),(1,3),(3,1)}) on (A={1,2,3}), which property does (R) have?If (R={(1,2),(2,1),(1,1),(2,2)}) on (A={1,2,3}), why is (R) not reflexive?If (R=A\times A) on (A={1,2,3}), which statement about (R) is correct?