Sets and Relations for JEE Main Mathematics
Sets and Relations establishes the language used throughout higher Mathematics. The questions are usually compact, but they test precise definitions: membership, subset, Cartesian product, relation properties, domain, range and function behaviour.
Scoring well requires disciplined notation. Write the universal set when complements are involved, list ordered pairs carefully in Cartesian products and test each property separately when a relation is given.
Topics to revise before solving
Sets and subsets
Roster form, set-builder form, cardinality and number of subsets.
Set operations
Union, intersection, difference, complement and De Morgan laws.
Power set
Count subsets and understand the set containing all subsets.
Cartesian product
Form ordered pairs and calculate the number of elements.
Relations
Check reflexive, symmetric, transitive and equivalence properties.
Functions
Domain, codomain, range, one-one, into and onto functions.
Sets and Relations formula recall
How to approach Sets and Relations questions
Translate notation into words
Before calculating, identify whether the question asks about membership, subset, union, complement, ordered pairs or a relation property.
Use small explicit lists when possible
For finite sets, listing elements or ordered pairs often prevents a notation mistake and makes the answer immediately visible.
Test relation properties independently
Do not assume a relation is equivalence because it looks symmetric. Check reflexive, symmetric and transitive one by one.
Check domain and codomain in functions
A relation becomes a function only when every domain element has one and only one image. Range can be smaller than codomain.
Sets and Relations Questions with Solutions
Try each question first. Open the solution only after writing your own reasoning.
If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then n(A ∩ B) equals:
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Answer: B. The common elements are 3 and 4. Thus A ∩ B = {3, 4}, so n(A ∩ B) = 2.
If A has 5 elements, then the number of elements in its power set P(A) is:
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Answer: D. A set with n elements has 2n subsets. Hence n(P(A)) = 25 = 32.
If A = {a, b} and B = {1, 2, 3}, then the number of elements in A × B is:
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Answer: C. n(A × B) = n(A)n(B) = 2 × 3 = 6. The ordered pairs are (a,1), (a,2), (a,3), (b,1), (b,2), (b,3).
For subsets A and B of a universal set U, (A ∪ B)' is equal to:
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Answer: B. By De Morgan's law, the complement of a union equals the intersection of the complements: (A ∪ B)' = A' ∩ B'.
If n(A) = 2 and n(B) = 3, then the number of relations from A to B is:
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Answer: D. A relation is any subset of A × B. Here n(A × B) = 2 × 3 = 6, so the number of subsets and hence relations is 26 = 64.
A relation R on a set A is called an equivalence relation if it is:
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Answer: C. All three properties are required. If even one condition fails, the relation is not an equivalence relation.
Which condition is necessary for a relation f from A to B to be a function?
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Answer: B. A function assigns exactly one output in B to each input in A. Onto functions have range equal to codomain, but that is not required for every function.
If n(A) = 20, n(B) = 15 and n(A ∩ B) = 5, then n(A ∪ B) is:
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Answer: C. n(A ∪ B) = 20 + 15 − 5 = 30. The intersection is subtracted because its elements were counted twice.
Continue your JEE Main Mathematics practice
After completing these questions, take a timed chapter test. Review wrong and guessed answers separately so that definitions and counting rules become automatic.
Try the Free Chapter TestCommon mistakes to avoid
- Treating ordered pairs (a, b) and (b, a) as the same pair.
- Forgetting that a set has distinct elements only.
- Using the complement without specifying or understanding the universal set.
- Counting common elements twice in a union problem.
- Checking only two out of three conditions for an equivalence relation.
- Confusing codomain with range.
- Calling a relation a function when one domain element has more than one image.
JEE Main Sets and Relations FAQs
Which Sets and Relations topics are important for JEE Main?
Revise set representation, set operations, De Morgan laws, subsets, power set, Cartesian product, relation properties, functions, one-one and onto functions, and composition of functions.
How can I test an equivalence relation quickly?
Check reflexivity for every element, symmetry for each related pair, and transitivity for every possible chain. All three conditions must hold.
What is the difference between range and codomain?
Codomain is the target set named in a function definition. Range is the set of outputs actually obtained. Therefore, range is always a subset of the codomain.
Are these official JEE Main previous-year questions?
No. These are original JEE Main-style practice questions written for concept revision and are not presented as official previous-year questions.