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 relation (R) contains ((3,5)) and (R) is symmetric, which pair must also be present?If relation (R) contains ((2,4)) and ((4,6)), and (R) is transitive, which pair must also be present?In which relation is it not necessary for any element to be related to itself?What is the inverse relation of (R={(1,2),(2,1)})?On (A={1,2,3}), which property is not present in (R={(1,1),(2,2),(3,3),(1,2)})?If (R={(1,1),(2,2),(3,3)}), what is its domain?If (R={(1,1),(2,2),(3,3)}), what is its range?If (A={1,2}) and (B={3}), what is (A\times B)?For (A={1,2}) and (B={3,4}), which pair will not be in (A\times B)?What are the domain and range of (R={(1,1),(1,2),(2,1),(2,2)})?If (A={1,2,3}) and (R={(1,1),(2,2),(3,3),(2,3)}), is (R) reflexive?Why is (R={(1,1),(2,2),(1,2),(2,1)}) not reflexive on (A={1,2,3})?If (R={(1,2),(2,1),(3,3)}), which pair is needed for symmetry because of ((1,2))?(R={(1,2),(2,1),(2,3)}) is not symmetric because which pair is missing?If (R={(1,2),(2,3),(1,3),(3,3)}), what is obtained for transitivity from ((1,2)) and ((2,3))?In (R={(1,2),(2,3),(3,4)}), which missing pair is first noticed for transitivity?If (A={1,2,3,4}), which pairs are in the smallest reflexive relation on (A)?If (A) has (5) elements, how many pairs are in the smallest reflexive relation on (A)?If (A) has (3) elements, how many pairs are in the universal relation on (A)?How many pairs are in the identity relation on (A={a,b,c})?