Shade the regions of a Venn diagram
"Shade the regions of a Venn diagram" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "Complement and De Morgan's laws" in Sets. U is Class XI-B's roll, 1 to 20. C is the cricket sign-ups and F the football sign-ups. Tap any region to shade it; the box below names the set you have shaded. (C ∪ F)′ = C′ ∩ F′: outside the union is the same as outside C and outside F. Likewise (C ∩ F)′ = C′ ∪ F′, which is 20 − 3 = 17 students here. The complement swaps ∪ and ∩. 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.
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
3 answers
- What does the "Shade the regions of a Venn diagram" simulation show?
- U is Class XI-B's roll, 1 to 20. C is the cricket sign-ups and F the football sign-ups. Tap any region to shade it; the box below names the set you have shaded.
- 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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