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 (A) has (4) elements, how many relations on (A) are both reflexive and symmetric?If (A) has (4) elements, what is the number of reflexive and antisymmetric relations on (A)?If (A) has (4) elements, how many relations on (A) are both symmetric and antisymmetric?If (A={1,2,3,4}) and (R={(1,2),(2,3),(3,4)}), how many pairs will be in the transitive closure of (R)?If (R={(1,2),(2,3),(3,4),(1,3),(2,4)}), which minimum pair must be added to make it transitive?For the partition ({{1,2},{3,4,5}}) of (A={1,2,3,4,5}), how many pairs are in the equivalence relation formed by it?For the partition ({{1},{2,3},{4,5}}) of (A={1,2,3,4,5}), how many pairs are in the equivalence relation formed by it?If (aRb) on (A={1,2,3,4,5,6}) when (a\equiv b \pmod{2}), how many pairs are in (R)?If (aRb) on (A={1,2,3,4,5,6,7,8}) when (a-b) is divisible by (3), what is the equivalence class of (2)?If (aRb) on (A={1,2,3,4,5,6,7,8}) when (a\equiv b \pmod{4}), what is the equivalence class of (1)?On (A={1,2,3,4,5}), if (aRb) when (a+b) is even, how many pairs are in (R)?On (A={1,2,3,4,5}), if (aRb) when (a+b) is odd, how many pairs are in (R)?On (A={1,2,3,6}), if (aRb) when (a) divides (b), how many pairs are in (R)?If divisibility relation is defined on (A={2,3,4,6,12}), which is the greatest element?If divisibility relation is defined on (A={2,4,6,12}), which is the least element?If divisibility relation is defined on (A={2,3,5,30}), which is the least element?If (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,4),(1,4)}) on (A={1,2,3,4}), what type of relation is (R)?Which transitivity requirement fails for R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3),(3,4),(1,3),(2,4)} on A={1,2,3,4}?If (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3)}) on (A={1,2,3}), which property definitely fails?If (R) is symmetric and ((3,5)\in R), which statement about (R^{-1}) is correct?