Venn Diagrams for Class 8 — Types of Sets (Subset, Overlapping & Disjoint Explained with Examples)

 

🎯 Venn Diagrams — Types of Sets (Subset, Overlapping & Disjoint)

Venn diagrams are a visual way to show how two sets relate to each other — whether they overlap, are completely separate, or one is contained inside the other. Each circle represents a set, and the shaded parts represent their relationships. Let’s study them one by one! 💡

Before You Begin:
Read the previous topic for better understanding: De Morgan’s Laws — Complement of Union and Intersection.

🔸 What is a Venn Diagram?

Venn diagrams show how sets are related. For two sets A and B inside a universal set U:

• A ∪ B (union) = elements in A or B or both.
• A ∩ B (intersection) = elements common to A and B.
• A′ (complement) = elements of U not in A.

🔹 Common Venn Shapes & What They Mean

Below are six common cases of Venn diagrams showing different relationships between sets A and B. Observe the diagrams carefully and note how the shapes represent union, intersection, and disjoint conditions.

① A is a Subset of B

When all elements of Set A are also in Set B, we say that A is a subset of B. This means A ⊂ B. In the Venn diagram, circle A lies completely inside circle B.

Fig (i): A is a subset of B — shaded area shows A ∪ B = B and A ∩ B = A.

Example:
Let A = {2,4,6}, B = {1,2,3,4,5,6}.
All elements of A are in B, so A ⊂ B.
Therefore, A ∩ B = A and A ∪ B = B.

② Sets A and B are Overlapping

When A and B share one or more common elements, they are called overlapping sets. The overlapping region represents A ∩ B (intersection), while the total shaded part shows A ∪ B (union).

Fig (ii): A and B are overlapping sets — this combined diagram shows both the union (A ∪ B) and intersection (A ∩ B) clearly.

Example:
A = {1,3,5,7}, B = {3,5,8,9}
⇒ A ∩ B = {3,5}, A ∪ B = {1,3,5,7,8,9}.

③ Sets A and B are Disjoint

If two sets have no elements in common, they are disjoint. Their intersection is the empty set (∅). In a Venn diagram, the circles do not touch or overlap.

Fig (iii): A and B are disjoint sets — no common elements, so A ∩ B = ∅. Both circles together show A ∪ B.

Example:
A = {2,4,6,8}, B = {1,3,5,7}
⇒ A ∩ B = ∅, A ∪ B = {1,2,3,4,5,6,7,8}.

④ Another Example — A is a Subset of B

This case also shows A ⊂ B with a different example. Notice that A is completely inside B, representing all elements of A included in B.

Fig (iv): A is a subset of B — second example. Here A lies completely inside B, so A ∪ B = B and A ∩ B = A.

⑤ Another Example — A and B Overlapping

Here again, A and B overlap, sharing some elements. This helps visualize how union and intersection work in different sets.

Fig (v): A and B overlap — second example showing intersection (A ∩ B) as the common region and union (A ∪ B) as the entire shaded area.

⑥ Another Example — A and B are Disjoint

Once again, A and B have no common elements. The two circles are separate, showing that their intersection is empty.

Fig (vi): A and B are disjoint sets — second example with no overlapping region, so A ∩ B = ∅ and A ∪ B covers both sets.

💡 Tip: Always label each part of your Venn diagram!

• Use shaded regions to show unions or intersections clearly.
• Draw circles neatly — it helps visualize the relationships better.
• For disjoint sets, remember there’s no common region at all.

🔔 Quick Notes (student tips)

• Start by writing the universal set U at the top corner — it helps when taking complements.
• Label each region (only A, only B, both A & B, outside both) to avoid mistakes.
• When asked for A ∪ B, include elements from both circles and the overlap; when asked for A ∩ B, include only overlap.

🧠 Practice Questions

1. Draw A ⊂ B and label A ∪ B and A ∩ B.
2. Draw overlapping sets A and B; list their intersection and union.
3. Draw disjoint sets; identify the null intersection.
4. Explain how A ∪ B and A ∩ B appear in overlapping sets.

Remember: Venn diagrams make complex relationships easy to see. Practice drawing them — once you understand the shapes, set operations become simple! 🌟

🎯 Venn Diagrams — Types of Sets Quiz

Check your understanding of subset, overlapping, and disjoint sets. 🌸

Q1: If every element of Set A is also in Set B, what kind of set is A in relation to B?

✅ A is a subset of B.

Q2: Two sets that share no common elements are called _______ sets.

✅ They are disjoint sets.

Q3: If Set A = {1, 2, 3} and Set B = {3, 4, 5}, what is their intersection?

✅ Intersection = {3}

Q4: What type of sets are A = {1,2,3} and B = {4,5,6}?

✅ They are disjoint sets (no common elements).

Q5: In a Venn diagram, overlapping circles represent what type of sets?

✅ They represent overlapping sets.

🔗 Explore Previous Topics from Sets Chapter

Let’s quickly revise the previous lessons from this chapter before you move ahead! 🌸 These topics together form the complete “Sets Chapter” — from understanding the basics to mastering Venn Diagrams.

📘 Understanding Sets in Mathematics 🧩 Recognition of Important Sets & Subsets 🔶 Operations on Sets — Union & Intersection ⚖️ De Morgan’s Laws — Complement of Union & Intersection

🌼 Keep learning with Math with Raabi — step-by-step, easy and colorful math lessons for Class 8 students!

© Math with Raabi — Sets Chapter Completed 🎯
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