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 (A={1,2,3}), if (aRb) when (a+b) is even, which statement is correct?On (A={1,2,3}), if (aRb) when (a+b) is odd, why is (R) not reflexive?On (A={1,2,3}), if (aRb) when (a) divides (b), which statement is correct?On (A={1,2,3}), if (aRb) when (a\ge b), what type of relation is (R)?If (R={(1,1),(2,2),(3,3),(4,4),(1,3),(3,1),(2,4),(4,2)}) on (A={1,2,3,4}), which partition is associated with (R)?If (R={(1,2),(2,1),(2,3),(3,2)}), what is (R^{-1})?If (R={(1,3),(2,3),(3,1)}), which is (R^{-1})?If (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}) on (A={1,2,3}), which pairs are still needed for equivalence?If (R) is the identity relation on (A={1,2,3,4}), how many pairs are in (R)?If the universal relation is on (A={1,2,3,4}), how many pairs will it contain?If (R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}) on (A={1,2,3}), why is (R) not an equivalence relation?If (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)}) on (A={1,2,3}), what is the correct name of (R)?If (R=\varnothing) on a non-empty set (A), which statement is correct?If (R) is symmetric on (A={1,2,3}) and ((2,3)\in R), which pair must be in (R)?If (R) is reflexive and (A={5,6,7}), which pair must be in (R)?If (R) is transitive and ((4,5)\in R), ((5,8)\in R), which pair must be in (R)?Let A={1,2,3}. If a symmetric relation R on A must contain (1,2), how many such relations are possible?If (A={1,2}), how many relations on (A) are both reflexive and symmetric?On (A={1,2,3}), relation (R) is defined by (aRb) if (|a-b|=0). What is (R)?On (A={1,2,3,4}), if (aRb) when (|a-b|) is even, what type of relation is (R)?