Master Set Representation in CBSE Class 11 Applied Mathematics. Learn to convert between Roster and Set-Builder forms with clear examples and exercises.
In Roster form, all elements of a set are listed, separated by commas, and enclosed within curly brackets { }. This method is ideal for finite sets where the number of elements is small and countable. For example, the set of all even natural numbers less than 10 is written as {2, 4, 6, 8}.
Step 1: Identify the condition: Natural numbers that are divisors of 12.
Step 2: List the numbers: 1, 2, 3, 4, 6, 12.
Step 3: Enclose in braces: {1, 2, 3, 4, 6, 12}.
Answer: {1, 2, 3, 4, 6, 12}
In Set-Builder form, we describe the elements of the set by a common property P(x) that every element x must satisfy. We use the notation {x : x satisfies property P}. This is particularly useful for infinite sets or sets with a large number of elements.
Step 1: Observe the pattern: 2¹, 2², 2³, 2⁴, 2⁵.
Step 2: Define the variable: x = 2ⁿ where n ∈ N.
Step 3: State the constraint: 1 ≤ n ≤ 5.
Answer: {x : x = 2ⁿ, n ∈ N, 1 ≤ n ≤ 5}
When representing sets, the order of elements does not matter, and elements should not be repeated. If an element is repeated in a description, it is written only once in the set. The universal set and empty set are fundamental concepts in this representation.
Step 1: Identify distinct elements: 1, 2, 3.
Step 2: Remove duplicates.
Step 3: Write in Roster form: {1, 2, 3}.
Answer: {1, 2, 3}