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
On integers, (aRb) iff (a-b) is divisible by (8). What is the equivalence class of (-3)?On integers, (aRb) iff (3a+4b) is divisible by (7). What type of relation is it?On integers, (aRb) iff (2a+2b) is divisible by (4). What type of relation is it?On integers, (aRb) iff (a+b) is even. What is the equivalence class of (1)?On real numbers, (aRb) iff (a-b\in\mathbb{Z}). What is the equivalence class of (\frac{1}{2})?On real numbers, (aRb) iff (a-b\in\mathbb{Q}). Which class is equal to ([\sqrt{2}])?On real numbers, (aRb) iff (a^2=b^2). What is the equivalence class of (0)?On real numbers, (aRb) iff (\lfloor a\rfloor=\lfloor b\rfloor). What type of relation is it?On real numbers, (aRb) iff (\lfloor a\rfloor=\lfloor b\rfloor). What is the equivalence class of (\frac{5}{2})?On real numbers, (aRb) iff (|a-b|=0). What type of relation is it?On real numbers, (aRb) iff (|a|<|b|). Which statement is correct?On real numbers, (aRb) iff (a^2+b^2=1). Which property does this relation satisfy?On (A={1,2,3,4,5}), (R={(a,b):a+b=6}). What type of relation is it?On (A={1,2,3,4,5}), (R={(a,b):a+b\le6}). Which statement is correct?On (A={1,2,3,4,5}), how many pairs are in (R={(a,b):a+b) is divisible by (4)(})?On (A={1,2,3,4,5,6}), how many pairs are in (R={(a,b):a-b) is divisible by (3)(})?On (A={1,2,3,4,5,6}), for (R={(a,b):\gcd(a,b)=1}), which of ((2,3)), ((2,4)), ((5,6)) belong to (R)?In the divisibility relation on (A={1,2,3,4,6,8,12,24}), what is the least upper bound of (6) and (8)?In the divisibility relation on (A={1,2,3,4,6,8,12,24}), what is the greatest lower bound of (8) and (12)?In the divisibility relation on (A={2,4,6,12,18}), how many maximal elements are there?