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 (R=\varnothing) on (A={1,2,3}), is (R) symmetric?If (R=\varnothing) on (A={1,2,3}), is (R) transitive?If (A) has (1) element, how many total relations are possible on (A)?If (A={1,2,3}) and (B={4,5}), how many pairs are there in (A\times B)?If (A={1,2,3}) and (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1)}), what must be added to make (R) universal?If (aRb) means (a) and (b) have the same parity, which conclusion is correct?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 (R^{-1})?If (R={(1,1),(2,2),(1,2),(2,1)}) on (A={1,2,3}), why is (R) not reflexive?If (R={(1,2),(2,3),(1,3),(3,3)}) on (A={1,2,3}), what is the main chain for transitivity?If (R={(1,1),(2,2),(3,3),(2,3),(3,2)}) on (A={1,2,3}), which statement about (R) is correct?If (R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,1)}) on (A={1,2,3,4}), choose the correct statement about (R).If (R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}) on (A={1,2,3}), why is (R) not symmetric?If a set has (5) elements, what is the total number of relations on it?If (A) has (4) elements, how many reflexive relations are possible on (A)?If (A={1,2,3}) and (R={(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)}), which property is definitely absent?If (R={(1,2),(2,3),(3,4)}), which pair first fills the gap for transitivity?If (R={(1,2),(2,3),(1,3),(3,4)}), which pair is still required for full transitivity?If (R={(1,1),(2,2),(3,3),(1,2),(2,1)}) on (A={1,2,3}), which partition is associated with this equivalence relation?On integers, (aRb) if (a-b) is divisible by (5). In which class will (7) lie?If on (A={1,2,3,4}), (aRb) if (a) and (b) are both even or both odd, what type of relation is (R)?