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)}) is a relation on the set (A={1,2}), what type of relation is it?How many ordered pairs are there in the empty relation on (A={1,2,3})?A set (A) has (4) elements. How many ordered pairs will the universal relation on (A) contain?If (R={(1,2),(2,1)}), what is the main property of this relation?On (A={1,2}), (R={(1,1),(1,2),(2,2)}) is given. Why is this relation reflexive?If a relation contains ((3,5)) but does not contain ((5,3)), which type can it definitely not be?On (A={1,2,3}), what is (R={(1,1),(2,2),(3,3)}) called?If (A={a,b}), how many ordered pairs are there in (A\times A)?A relation from two sets (A) and (B) is a subset of what?If (A) has (3) elements, how many different relations can be formed on (A)?For (R={(1,2),(2,3),(1,3)}) on (A={1,2,3}), which property is visible?If ((1,2)) and ((2,3)) are in a relation but ((1,3)) is not, which property fails?On (A={1,2}), (R={(1,1),(2,2),(1,2),(2,1)}) is equal to which relation?Which condition is necessary for a relation to be reflexive?Which condition is correct for a relation to be symmetric?When is a relation called transitive?Which relation is reflexive on A={1,2,3}?If (R={(2,2),(3,3),(2,3),(3,2)}), which pair is required for symmetry because of ((2,3))?For (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), which property is definitely present?If relation (R) contains only ((1,2)), is it reflexive on (A={1,2})?