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 (3) elements, how many antisymmetric relations can be formed on (A)?If (A) has (4) elements, how many relations are reflexive and symmetric but not antisymmetric?On (A={1,2,3,4}), how many relations are reflexive and therefore cannot be irreflexive?On (A={1,2,3}), how many relations are neither symmetric nor antisymmetric?On (A={1,2,3,4,5}), how many equivalence relations have exactly four equivalence classes?On (A={1,2,3,4,5}), how many equivalence relations have exactly three equivalence classes?If (A={1,2,3,4}), how many equivalence relations have (1) and (2) in the same class?If (A={1,2,3,4}), how many equivalence relations have (1) and (2) in different classes?On integers, (aRb) iff (2a+3b) is divisible by (5). In which property does this relation fail?On integers, (aRb) iff (a+2b) is divisible by (4). Which statement is correct?On real numbers, (aRb) iff (a-b\in\mathbb{Z}) and (a+b\in\mathbb{Z}). What type of relation is it?On real numbers, (aRb) iff (a-b\in\mathbb{Q}). What is the equivalence class of (\sqrt{2})?On real numbers, (aRb) iff (a-b\in\mathbb{Q}). Which of the following classes is equal to ([0])?On real numbers, (aRb) iff (a^2-b^2=0). What is the equivalence class of (3)?On real numbers, (aRb) iff (a^3-b^3=0). What is the equivalence class of (2)?On real numbers, (aRb) iff (|a-b|\le 1). In which property does this relation fail?On real numbers, (aRb) iff (|a-b|<1). What type of relation is it?On real numbers, (aRb) iff (a-b>1). Which statement is correct?On real numbers, (aRb) iff (ab>0). What type of relation is it?On real numbers, (aRb) iff (ab\ge0). In which property does this relation fail?