Mathematics
Relations that are reflexive and symmetric
प्रतिवर्ती और सममित संबंध
In this Class 11 Mathematics topic from Relations and Functions, students learn to identify and define reflexive and symmetric relations on a set. They examine conditions such as every element being related to itself for a reflexive relation and the reversal of an ordered pair for a symmetric relation. Using ordered pairs, sets, tables, and everyday examples, students practise testing relations, distinguishing the two properties, and explaining their conclusions clearly.
Practice questions
If A has 3 elements, how many symmetric relations on A are also reflexive?MediumLevel 3If A={1,2,3} and R={(1,2),(2,1),(2,3)}, why is R not symmetric?EasyLevel 26If R = {(1, 4), (4, 1), (2, 2)}, is R symmetric?EasyLevel 27On A={1,2,3}, which type is the relation R={(1,1),(2,2),(3,3),(1,2)}?MediumLevel 25On A={1,2,3}, what type is R={(1,1),(2,2),(3,3),(1,2),(2,1)}?MediumLevel 25On A={1,2,3,4}, if aRb means a≤b, which property must this relation have?MediumLevel 25If A={1,2,3,4,5,6} and aRb when a≡b (mod 3), what is the equivalence class of 1?MediumLevel 25If A={1,2,3} and R={(1,1),(2,2),(3,3)}, what type of relation is R?EasyLevel 26If R = {(1, 2), (2, 1), (3, 3)}, what is the main reason that R is symmetric?MediumLevel 26For R = {(a,b): |a − b| ≤ 1} on A = {1,2,3,4}, which statement is correct?HardLevel 25Which is the identity relation I_A on A = {1,2,3}?MediumLevel 25What is R = {(a,b): a² = b²} on A = {-2,-1,1,2}?HardLevel 25On A = {0, 1, 2, 3, 4, 5, 6, 7}, define aRb if and only if a − b is divisible by 4. How many equivalence classes are there?MediumLevel 27On A = {1,2,3,4}, let R = {(a,b) : a divides b}. Which statement about R is correct?HardLevel 25If A has 3 elements, how many relations on A are both reflexive and symmetric?MediumLevel 25On A = {1,2,3,4,5,6}, let R = {(a,b) : gcd(a,b) = 1}. Which property is correct for this relation?HardLevel 26For A = {1,2,3,4}, let R = {(a,b) : a+b=5}. What is the correct statement about R?MediumLevel 27