दैनिक पाठ योजना – Sets | Grade 8

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Concepts

Start here — understand the core ideas before practising.

What is a Set? (समूह के हो?)

A set is a well-defined collection of distinct objects, called members or elements. We write sets using curly braces { }.

A = {1, 2, 3} B = {a, b, c} C = {चिनी, नुन, मर्च}

Key Vocabulary

Element (सदस्य): An item inside a set. Example: 2 ∈ A
Universal Set (सार्वत्रिक समूह): The set of all elements under consideration.
Intersection (प्रतिच्छेद ∩): Elements shared by both sets.
Union (मिलन ∪): All elements in either set.

Disjoint Sets — अलगिएका समूह

📌 Definition Two sets are disjoint if they share no common element — their intersection is empty: A ∩ B = { } = ∅

Examples

✅ A = {2, 4, 6} and B = {1, 3, 5} — no shared element → Disjoint

✅ P = {a, b} and Q = {c, d} — no shared element → Disjoint

✅ M = {10, 20} and N = {30, 40} — no shared element → Disjoint

🔵 In a Venn diagram, disjoint sets appear as two separate circles that do not touch.

Overlapping Sets — खप्टिएका समूह

📌 Definition Two sets are overlapping if they share at least one common element — their intersection is non-empty: A ∩ B ≠ ∅

Examples

✅ X = {मर्च, नुन, चिनी} and Y = {चिनी, चियापत्ती, दूध} — shared: चिनी → Overlapping

✅ A = {1, 2, 3} and B = {3, 4, 5} — shared: 3 → Overlapping

✅ M = {10, 20} and N = {20, 30} — shared: 20 → Overlapping

🔵 In a Venn diagram, overlapping sets appear as two circles that partially overlap.

Quick Comparison

Feature	Disjoint Sets	Overlapping Sets
Common elements	None (∅)	At least one
Intersection	A ∩ B = ∅	A ∩ B ≠ ∅
Venn diagram	Separate circles	Overlapping circles

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Venn Diagrams

Visual representations of sets — hover circles to explore!

Disjoint Sets

A = {2, 4, 6} | B = {1, 3, 5}

No shared elements → Disjoint

Overlapping Sets

A = {1,2,3} | B = {3,4,5}

Shared element: 3 → Overlapping

🍽️ Real-life Example — Kitchen Sets

X = {मर्च, नुन, चिनी} Y = {चिनी, चियापत्ती, दूध}

📝 Homework Example

If M = {10, 20} and N = {20, 30} — are they disjoint or overlapping?

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MCQ Quiz

10 multiple-choice questions — click an option to answer.

0 / 10

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10/10

Excellent!

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Fill in the Blanks

Type the correct word or symbol in each blank.

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Match the Pairs

Click a term on the left, then click its matching definition on the right. (10 pairs)

Terms

Definitions

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Problem Solving

10 step-by-step worked examples — show or hide each solution!