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
For the relation on A={1,2,3,4} whose equivalence classes are {1,2} and {3,4}, which pair is definitely absent?On (A={1,2,3,4}), if (aRb) when (a\le b), how many pairs are in (R)?On (A={1,2,3,4}), if (aRb) when (a<b), how many pairs are in (R)?On (A={1,2,3,4}), if (aRb) when (a<b), which statement is correct?On (A={1,2,3,4}), if (aRb) when (a\le b), which statement is correct?If (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,4),(4,3)}) on (A={1,2,3,4}), which partition is formed by (R)?If the classes of (R) on (A={1,2,3,4}) are ({1,2}) and ({3,4}), which pair must be in (R)?How many ordered pairs does the equivalence relation with classes {1,2} and {3,4} contain?If (R) is symmetric on (A={1,2,3}) and ((1,3)) is in (R\circ R), what type of chain may be possible?If (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4),(1,4)}) on (A={1,2,3,4}), which statement about (R) is false?If (A) has (4) elements, how many antisymmetric relations can be formed on (A)?If (A) has (5) elements, what is the number of relations on (A) that are both reflexive and antisymmetric?How many relations on (A={1,2,3,4}) are both symmetric and antisymmetric?How many relations on (A={1,2,3,4}) are reflexive, symmetric and antisymmetric all together?If (A) has (4) elements, how many equivalence relations can be formed on (A)?On (A={1,2,3,4}), how many equivalence relations have exactly two equivalence classes?On (A={1,2,3,4,5}), how many equivalence relations have one class of size (2) and the other of size (3)?On (A={1,2,3,4}), how many equivalence relations have exactly one class of size (2) and all other classes singleton?On integers, (aRb) iff (a-b) is divisible by (6). What is the equivalence class of (7)?On integers, (aRb) iff (a+2b) is divisible by (3). In which property does this relation fail?