Unit 5 Sets And Functions Comprehensive Solutions

Sets and functions are key concepts in mathematics, serving as the building blocks for various mathematical theories and applications. In Unit 5 Sets and Functions of Class 10 math, students will learn about the fundamental properties and types of sets, such as finite and infinite sets, subsets, and the universal set. They’ll also explore set operations like union, intersection, and set difference, as well as visualize relationships through Venn diagrams. Additionally, this unit covers the Cartesian product, relations, and functions, helping students understand how sets and functions work together to describe mathematical relationships. By engaging with these concepts, students will gain a clear understanding of how sets and functions organize information and model real-world situations.

Multiple Choice Questions Test for Unit 5

To reinforce your understanding of Unit 5 Sets and Functions, we have included a multiple-choice quiz. This quiz covers all the essential topics, including types of sets, operations on sets, relations, and functions. The questions are designed to help you review key points and assess your grasp of these concepts.

Unit 5 MCQs Test for 10 Class Math

1 / 20

A collection of well-defined objects is called

subset

power set

set

none of these

2 / 20

A set $Q = \left\{ \frac{a}{b} \ | \ a, b \in Z \land b \neq 0 \right\}$ is called a set of

whole numbers

natural numbers

irrational numbers

rational numbers

3 / 20

The different number of ways to describe a set are

4 / 20

A set with no element is called

subset

empty set

singleton set

super set

5 / 20

The set $\{ x \ | \ x \in W \land x \leq 101 \}$ ${x ∣ x \in W \land x \leq 101}$ is

infinite set

subset

null set

finite set

6 / 20

The set having only one element is called

null set

power set

singleton set

subset

7 / 20

Power set of an empty set is

{∅}

{a}

{∅, {a}}

∅

8 / 20

The number of elements in power set {1, 2, 3} is

9 / 20

If $A \subseteq B$ , then $A \cup B$ is equal to

∅

none of these

10 / 20

If $A \subseteq B$ , then $A \cap B$ is equal to

∅

none of these

11 / 20

$if A \subseteq B$ , then $A - B$ is equal to

∅

B-A

12 / 20

$(A \cup B) \cup C$ is equal to

A∩(B∪C)

(A∪B)∩C

𝐴 ∪ ( 𝐵 ∪ 𝐶 )

𝐴 ∩ ( 𝐵 ∩ 𝐶 )

13 / 20

$A \cup (B \cap C)$ is equal to

(A∪B)∩(A∪C)

A∩(B∩C)

(A∩B)∪(A∩C)

A∪(B∪C)

14 / 20

If A and B are disjoint sets, then $A \cup B$
is equal to

∅

B∪A

15 / 20

If number of elements in set A $A$ is 3 and in set $B$

is 4,
then the number of elements in

$A \times B$

16 / 20

If the number of elements in set A

$A$

is 3 and in set

$B$

is 2,
then the number of binary relations in $A \times B$ is

$2^3$

$2^6$

$2^8$

$2^2$

17 / 20

The domain of $R = {(0, 2), (2, 3), (3,3), (3, 4)}$ is

{0, 3, 4}

{0, 2, 3}

{0, 2, 4}

{2, 3, 4}

18 / 20

The range of $R = \{ (1, 3), (2, 2), (3, 1), (4, 4) \}$ is

{1, 2, 4}

{2, 3, 4}

{1, 2, 3, 4}

{1, 3, 4}

19 / 20

Point (-1,4) lies in the quadrant

III

20 / 20

The relation {(1,2),(2,3),(3,3),(3,4)} is

onto function

into function

not a function

one-one function

Your score is

Unit 5 Sets and Functions Key-Points

Sets and Functions form a fundamental part of mathematics, providing the foundational language and tools for various branches. In unit 5 of Class 10 math, students will explore the following concepts:

Definition of a Set:

Set: A well-defined collection of distinct objects, considered as an object in its own right.

Types of Sets:

Empty Set (Null Set): A set with no elements, denoted by {} or ∅.
Singleton Set: A set with exactly one element.
Finite Set: A set with a countable number of elements.
Infinite Set: A set with an uncountable number of elements.
Equal Sets: Two sets with exactly the same elements.
Equivalent Sets: Two sets with the same number of elements.
Subset: Set A is a subset of set B if every element of A is also an element of B.
Proper Subset: Set A is a proper subset of set B if A is a subset of B and A ≠ B.
Universal Set: The set that contains all objects or elements under consideration.
Power Set: The set of all subsets of a set, including the empty set and the set itself.

Operations on Sets:

Union (A ∪ B): A set containing all elements that are in A, or B, or both.
Intersection (A ∩ B): A set containing all elements that are both in A and B.
Set Difference (A – B): A set containing elements in A that are not in B.
Complement of a Set (A’): Elements not in set A, but in the universal set.

Venn Diagrams:

Visual representations of sets and their relationships using overlapping circles.

Cartesian Product of Sets:

Cartesian Product (A × B): The set of all ordered pairs where the first element is from A and the second is from B.

Relations:

Relation: A subset of the Cartesian product of two sets, describing how elements of one set relate to elements of another.

Functions:

Function (Mapping): A relation where each element of the domain is associated with exactly one element of the co-domain.
Domain: The set of all possible inputs for the function.
Co-domain: The set of potential outputs.
Range: The actual set of outputs produced by the function.

Types of Functions:

One-to-One Function (Injective): Each element of the domain maps to a unique element of the co-domain.
Onto Function (Surjective): Every element of the co-domain is the image of at least one element from the domain.
Bijective Function: Both one-to-one and onto; establishes a perfect “pairing” between the domain and co-domain.

Graphical Representation of Functions:

Plotting functions on the Cartesian plane to visualize their behavior.

Real-life Applications:

Understanding how sets and functions model real-world scenarios, such as organizing data, computer science algorithms, and more.

Deepen your understanding of this unit by checking its important formulas.

Unit 5 Sets and Functions table of symbols used in unit 5 and their explanation.

Unit 5 Sets and Functions provides essential tools for understanding mathematical relationships, laying the groundwork for more advanced topics in algebra, calculus, and beyond. Mastering these topics will not only help students tackle higher-level math problems but will also develop their logical thinking and problem-solving skills. As students progress, they can explore more about functions and real-life applications of sets, helping them see the relevance of these topics in fields like computer science, data organization, and science.

For further practice, visit our page on Class 10 math exercises for additional resources and solutions. If you have completed the solutions of Unit 5 Sets and Functions, let’s move on to the solution of unit 6. For a comprehensive overview of sets and their applications, you might also find it helpful to explore this introductory guide on sets and functions. Through these resources, students will gain a deeper appreciation of sets and functions, essential for a solid foundation in mathematics.

Unit 5 Sets and Functions Comprehensive Solutions

Multiple Choice Questions Test for Unit 5

Unit 5 Sets and Functions Key-Points

Unit 1 Quadratic Equations: Empowering Solutions

Unit 12 Angle in a Segment of a Circle Master Solutions

Unit 4 Partial Fractions

Master Exercise 2.5 Class 10 with Ease

Notes of 10th Class Math (Science Group) – Your Guide to Success

Exercise 2.4 Class 10 Solutions Complete Guide

Leave a Reply Cancel reply

Multiple Choice Questions Test for Unit 5

Unit 5 Sets and Functions Key-Points

Similar Posts

Leave a Reply Cancel reply