XI Math Chapter 1: Sets Worksheet (Basic)

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the minimum number of elements in ∪ 2 if 2 = 6?

9 (correct)

If A is a set containing 6 elements, what is the number of non-empty subsets of A?

63 (correct)

If = ∅, what is the number of elements in /?

Unknown

Zero

Equal to the number of elements in (correct)

Infinite

What is the set E in roster form?

{E, F, G, H, I, J, K, L, M} Signup and view all the answers

What is the set F in set builder form?

{x: x ∈ N, x ≤ 10} Signup and view all the answers

What is the interval form of the set {x: x ∈ O, −4 ≤ x < 6}?

(-4, 6) Signup and view all the answers

If ⊂ 2, what can be concluded about ℎ 6 − 2?

ℎ 6 − 2 is equal to 6 − Signup and view all the answers

If / = / 2 , what can be concluded about #ℎ B ℎ?

#ℎ B ℎ is equal to 2 Signup and view all the answers

What is the total number of people who read at least one of the newspapers?

52 Signup and view all the answers

How many people read exactly one newspaper?

19 Signup and view all the answers

If a set A contains elements from 1 to 10, what is the cardinality of A?

10 Signup and view all the answers

In set theory, what does the symbol ∩ represent?

Intersection of sets Signup and view all the answers

Which of the following subsets belongs to the set if D = {a, b, c}?

{a, b, c} Signup and view all the answers

When given two sets, which operation results in the elements that are in both sets?

Intersection Signup and view all the answers

What is the value of the intersection of any set with itself?

The set itself Signup and view all the answers

If sets A, B, and C have the sizes 15, 22, and 14, respectively, with their intersections provided, what is the value of A ∪ B ∪ C given N = 35?

30 Signup and view all the answers

If A = {x | x is a positive integer less than 10 and 2x - 1 is an odd number}, which of the following is the correct roster form of A?

{1, 3, 5, 7, 9} Signup and view all the answers

What is the power set of the set {1, 2}?

{{}, {1}, {2}, {1, 2}} Signup and view all the answers

If a set has 2 elements, what would be the result for |A| + |B| if both sets are finite?

2 Signup and view all the answers

How many students were taking neither apple juice nor orange juice from a survey of 400 students, with given details about those taking each?

100 Signup and view all the answers

How many individuals were exposed to both chemicals C1 and C2 among individuals with a skin disorder?

30 Signup and view all the answers

If two sets intersect such that A ∩ B = A and A is a proper subset of B, which statement is true?

B contains all elements of A plus additional elements. Signup and view all the answers

Study Notes

Sets Overview

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

Types of Questions

Multiple Choice Questions

Questions often assess understanding of set operations, such as union (∪), intersection (∩), and complements.
Familiarize with examples like calculating union of sets based on provided cardinalities and intersections.

Fill in the Blanks

Common equations involve properties of finite sets, such as the relation between their union and intersections.
Understand that the power set of a set with n elements contains 2^n subsets.

Set Representation

Roaster form lists all elements (e.g., A = {1, 2, 3}).
Set builder form defines sets by a condition (e.g., B = {x | x is an even integer}).

Problem Solving Techniques

Short Answer Questions

Involve proof or demonstration of set properties using definitions.
Practice problems involving manipulation of set operations and cardinality.

Long Answer Questions

Require application of set theory to real-world scenarios, like surveys.
Example: Finding the number of elements in either or neither of overlapping sets using inclusion-exclusion principle.

Important Concepts

Power Set: The set of all subsets of a set, crucial for understanding combinations and set operations.
Union and Intersection: Fundamental operations; union combines all elements from both sets, while intersection finds common elements.
Real-life Applications: Sets are often used to categorize data, like survey responses, which help analyze the relationships between groups.

Survey and Data Interpretation

Use Venn diagrams for visual representation when dealing with multiple sets and their relationships.
Example: If 400 students take juice, use a Venn diagram for apple and orange to find those taking neither.

Practice Questions

Create examples for individual practice, focusing on filling in blanks, multiple-choice answers, and set representation in variations.
Explore the applications of set theory in everyday situations for better understanding.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

Test your understanding of sets with this basic worksheet, covering concepts like union and intersection of sets. For XI class math students.