BLE Grade 8 Math: Sets Solutions (Weightage: 3 Marks)

Prepared by Kailash Pahari

Class 8 Math Sets: Theoretical Concepts & Formulas

Prepared by Kailash Pahari — Essential definitions, methods, and subset formulas for BLE Grade 8 Sets

A set is a well-defined collection of distinct objects or elements.

A set is denoted by capital letters (A, B, C) and elements are enclosed within curly brackets { }.

1. Description Method: Describing members in words.
Ex: A = {Vowels in English alphabet}
2. Listing / Roster Method: Listing elements separated by commas.
Ex: A = {a, e, i, o, u}
3. Set-Builder Method: Stated using a variable rule.
Ex: A = {x : x is a vowel in English alphabet}

Given set A = {y, e, s}, cardinality n(A) = 3.

1. Total Subsets (2ⁿ = 2³ = 8):

∅, {y}, {e}, {s}, {y, e}, {e, s}, {y, s}, {y, e, s}

2. Proper Subsets (2ⁿ - 1 = 7):

∅, {y}, {e}, {s}, {y, e}, {e, s}, {y, s}

3. Improper Subset (1):

{y, e, s} (The set itself)

Two or more sets having at least one common element are called overlapping sets.

Example: A = {1, 2, 3}, B = {3, 4, 5}
Here, A ∩ B = {3} ≠ ∅ (Element 3 is common).

Two or more sets having no common elements at all are called disjoint sets.

Example: A = {1, 2}, B = {4, 5}
Here, A ∩ B = ∅ (No shared elements).

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