Master the concept of well-defined sets in CBSE Class 11 Applied Mathematics. Learn to identify, represent, and classify collections with examples.
A set is a well-defined collection of distinct objects. An object is well-defined if there is a clear criterion to decide whether it belongs to the collection or not. For example, the collection of all prime numbers less than 10 is a set {2, 3, 5, 7}.
Step 1: Analyze the collection 'The collection of all talented students in your class'.
Step 2: Determine if 'talented' is a well-defined criterion.
Step 3: Since talent is subjective and varies from person to person, it is not well-defined.
Answer: The collection is not a set.
Sets are usually denoted by capital letters like A, B, or S. The elements are enclosed within curly braces { } and separated by commas. The order of elements does not matter, and elements should not be repeated.
Step 1: Identify the letters in the word: M, A, T, H, E, M, A, T, I, C, S.
Step 2: Extract the vowels: A, E, I.
Step 3: List them without repetition.
Answer: {A, E, I}
The number of distinct elements in a set is called its cardinality, denoted by n(A). If a set contains no elements, it is called an empty set, denoted by ∅ or { }.
Step 1: List the elements satisfying the condition: 1, 2, 3, 4, 5.
Step 2: Count the number of elements.
Step 3: n(A) = 5.
Answer: 5