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}), how many pairs are in the largest relation?If (A) has (3) elements, what is the number of total relations on (A)?If (A) has (2) elements and (B) has (3) elements, how many total relations are there from (A) to (B)?What is the domain of the relation (R={(1,2),(2,3)})?What is the range of the relation (R={(1,2),(2,3),(3,3)})?In (R={(1,2),(2,4),(3,6)}), which element is not in the range?If (R={(a,1),(b,2)}), what is the domain of (R)?If (R={(a,1),(b,2),(c,2)}), what is the range of (R)?What is the inverse relation of (R={(1,1),(1,2),(2,2)})?If (R) is symmetric, what is the relation between (R) and (R^{-1})?On (A={1,2}), what type of relation is (A\times A)?On (A={1,2,3}), which property does (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) have?Which property is clearly visible in (R={(1,2),(2,1),(2,3),(3,2)})?Why is (R={(1,2),(2,3)}) not transitive?If (R={(1,1),(2,2),(1,2),(2,1)}) on (A={1,2}), what relation is it?In which relation is every element considered related only to itself?On (A={1,2,3,4}), how many pairs are in the smallest reflexive relation?If (A) has (4) elements, how many pairs are there in (A\times A)?For (R={(1,1),(2,2),(3,3)}) on (A={1,2,3}), which statement is correct?In (R={(1,1),(2,2),(1,2),(2,1)}), which property is indicated by having ((1,2)) and ((2,1)) together?