Sets - Introduction

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Questions and Answers

Which of the following collections can be definitively listed and is therefore considered a set?

Planets in our solar system. (correct)
Happy children in the village.
Brilliant students of the class.
Brave children in the class.

What is a fundamental characteristic of a collection that qualifies it to be defined as a 'set'?

The collection must be large.
The collection must contain diverse items.
The elements of the collection can be clearly listed. (correct)
The elements must have a monetary value.

Why are collections described by subjective terms like 'happy' or 'brilliant' generally not considered sets in a mathematical context?

Because the number of elements is too large.
Because such collections do not exist in reality.
Because the criteria for inclusion are not well-defined and vary from person to person. (correct)
Because these qualities change over time.

Which of these collections would universally be accepted as a 'set'?

The first ten even numbers. (C) Signup and view all the answers

Why is the collection of 'strong forts of Maharashtra' not considered a well-defined set?

Because the definition of 'strong' is subjective and varies. (C) Signup and view all the answers

Which of the following is an example of a set?

Collection of months in a year. (B) Signup and view all the answers

Consider the collection of 'first 10 counting numbers.' Which of the following statements accurately describes this collection?

It forms a set because its elements are clearly defined and finite in this context. (B) Signup and view all the answers

Classify which of the following would NOT be considered a set?

Skilled musicians in a city. (C) Signup and view all the answers

What differentiates a 'set' from a general collection of objects?

Sets require clearly defined criteria for membership. (B) Signup and view all the answers

Which of the following best illustrates the concept of a 'Universal set'?

A set containing all the elements currently under consideration. (B) Signup and view all the answers

Consider set A = {2, 4, 6, 8} and set B = {6, 8, 10, 12}. Which elements would be part of the 'intersection' of sets A and B?

{6, 8} (C) Signup and view all the answers

What is the 'union' of two sets?

All distinct elements present in either set. (A) Signup and view all the answers

Which visual aid is most commonly used to represent sets and their relationships, such as intersections and unions?

Venn diagrams (D) Signup and view all the answers

If Set A represents all even numbers and Set B represents all multiples of 3, how would you describe the intersection of Set A and Set B?

All multiples of 6. (A) Signup and view all the answers

Given set P = {1, 3, 5, 7, 9} and set Q = {2, 3, 5, 8}, what is the union of P and Q?

{1, 2, 3, 5, 7, 8, 9} (B) Signup and view all the answers

If A = {1, 2, 3, 4, 5} and B = {3, 4, 5}, which statement correctly describes the relationship between A and B?

B is a subset of A. (D) Signup and view all the answers

If set C = {x | x is a vowel in the English alphabet}, what are the elements of set C?

{a, e, i, o, u} (C) Signup and view all the answers

How would you visually represent a scenario where two sets, X and Y, have no elements in common?

Two separate, non-intersecting circles in a Venn diagram. (C) Signup and view all the answers

Consider the sets A = {1, 2, 3} and B = {3, 2, 1}. Which of the following statements is true?

A and B are equal sets. (C) Signup and view all the answers

If set A contains the first 5 positive integers and set B contains the first 5 prime numbers, what number of elements would be available in the union of A and B?

9 (A) Signup and view all the answers

Flashcards

What is a 'Set'?

A well-defined collection of objects.

What is NOT a set?

A collection where the description is subjective and varies from person to person.