Sets

Maths · Class 11

Simulation · Maths · Class 11

The complement depends on U

"The complement depends on U" is a free, interactive Class 11 Maths simulation for JEE, built on the NCERT section "Complement and De Morgan's laws" in Sets. A = even numbers drawn on a number line; switching the universal set (N, Z, {1,…,20}) redraws A′ so the complement visibly changes while A does not. JEE Main asked 3 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).

From the lesson Complement and De Morgan's laws in Sets. Change the values and watch what happens.

The complement depends on UMaths · Class 11

What it shows

NCERT §1.10

A = even numbers drawn on a number line; switching the universal set (N, Z, {1,…,20}) redraws A′ so the complement visibly changes while A does not.

Controls

3 to try

  • SegmentedU = N / Z / {1,…,20}
  • Slidervisible window −20 to 20
  • Toggleshow A / show A′

Try this

Pick the universal set in which −3 belongs to A′ (U = Z) and then the one in which A′ has exactly 10 elements (U = {1,…,20}).

Common mistake

Finding a complement without fixing the universal set.

In JEE Main

42 shifts analysed

3 questions from Sets across the 42 JEE Main shifts Lumi has analysed (2017–2026).

The idea behind it

NCERT §1.10

  • The complement of A with respect to U is A′ = {x : x ∈ U and x ∉ A} = U − A: everything in the universal set that is outside A. A′ is itself a subset of U, and it changes if U changes.
  • Complement laws: A ∪ A′ = U and A ∩ A′ = φ. Double complement: (A′)′ = A. Also φ′ = U and U′ = φ.
  • De Morgan's laws: (A ∪ B)′ = A′ ∩ B′ and (A ∩ B)′ = A′ ∪ B′. Taking the complement swaps ∪ and ∩ and puts a dash on each set.
  • Check with U = {1, …, 6}, A = {2, 3}, B = {3, 4, 5}: A ∪ B = {2, 3, 4, 5}, so (A ∪ B)′ = {1, 6}; A′ = {1, 4, 5, 6} and B′ = {1, 2, 6}, so A′ ∩ B′ = {1, 6} as well.
  • In a Venn diagram A′ is the part of the rectangle outside A's circle, and (A ∪ B)′ is the region outside both circles.
  • A useful rewrite that follows from the definitions: A − B = A ∩ B′, the part of A that is also outside B.

Questions

4 answers

What does the "The complement depends on U" simulation show?
A = even numbers drawn on a number line; switching the universal set (N, Z, {1,…,20}) redraws A′ so the complement visibly changes while A does not.
What mistake does the "The complement depends on U" simulation fix?
A common mistake it clears up: finding a complement without fixing the universal set.
Does JEE Main ask questions from Sets?
Yes. JEE Main asked 3 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
Is this simulation free?
Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Complement and De Morgan's laws" in Sets (Class 11 Maths).

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