Sets and Relation questions
385 published questions with worked solutions.
- Consider the relation R on the set −2, −1, 0, 1, 2 defined by (a, b) ∈ R if and only if 1 + ab > 0. Then, among the statements:...
- Let A = 2, 3, 6, 7 and B = 4, 5, 6, 8 . Let R be a relation defined on A × B by (a₁, b₁) R (a₂, b₂) if and only if a₁ + a₂ = b₁ +...
- Let A and B be two finite sets with m and n elements respectively. The total number of subsets of the set A is 56 more than the...
- Let S = 1, 2, 3, …, 10 . Suppose M is the set of all the subsets of S, then the relation R = (A, B) : A ∩ B ≠ φ ; A, B ∈ M is:
- If R is the smallest equivalence relation on the set 1, 2, 3, 4 such that (1, 2), (1, 3) ⊂ R, then the number of elements in R is...
- Let R be a relation on Z × Z defined by (a, b) R (c, d) if and only if ad – bc is divisible by 5. Then R is
- The number of symmetric relations defined on the set 1, 2, 3, 4 which are not reflexive is ________.
- A group of 40 students appeared in an examination of 3 subjects – Mathematics, Physics and Chemistry. It was found that all...
- Let A = 1, 2, 3, …., 100 . Let R be a relation on A defined by (x, y) ∈ R if and only if 2x = 3y. Let R₁ be a symmetric relation...
- Let A = 1, 2, 3, 4 and R = (1, 2), (2, 3), (1, 4) be a relation on A. Let S be the equivalence relation on A such that R ⊂ S and...
- Let A = 2, 3, 4, 5, ...., 30 and ' ' be an equivalence relation on A × A, defined by (a, b) (c, d), if and only if ad = bc. Then...
- Define a relation R over a class of n × n real matrices A and B as "ARB iff there exists a non-singular matrix P such that PAP^...
- The number of subsets of 1,2,3, ,9 containing at least one odd number is
- Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A B having 3 or more elements...
- Let N be the set of natural number and a relation R on N be defined by R= (x,y) N N:x^3-3x^2y-xy^2+3y^2=0
- If A = [x R:|x – 2|>1 , B = x R: x^2-3 >1 , C = x R:|x-4| 2 and Z is the set of all integers, then the number of subsets of the...
- Let Z be the set of all integers, A = (x,y) Z Z : (x-2)^2+y^2 4 , B = (x,y) Z Z : x^2+y^2 4 and C = (x,y) Z Z : (x-2)^2+(y-2)^2 4...
- Which of the following is not correct for relation R on the set of real numbers ?
- Out of all the patients in a hospital 89% are found to be suffering from heart ailment and 98% are suffering from lungs...
- Let R = (P, Q) | P and Q are at the same distance from the origin be a relation, then the equivalence class of (1,–1) is the set :
Other chapters
Alcohols, Phenols and EthersAldehydes, Ketones and Carboxylic AcidsAlternating CurrentAminesAnatomy of Flowering PlantsAncient Indian HistoryAnimal KingdomApplication of DerivativesArea Under CurveAromatic Compounds and Aryl HalidesAtomsBasic Mathematics and LogarithmBinomial TheoremBiodiversity and ConservationBiological ClassificationBiomoleculesBiotechnology and Its ApplicationsBiotechnology: Principles and ProcessesBody Fluids and CirculationBreathing and Exchange of GasesCell Cycle and Cell DivisionCell: The Unit of LifeChemical Bonding and Molecular StructureChemical Coordination and Integration