Mathematics Set Theory Quiz

Study Notes

Roster Form Sets

Set of integers from -3 to 5: {-3, -2, -1, 0, 1, 2, 3, 4, 5}
Set of natural numbers which are multiples of 5 and less than 30: {5, 10, 15, 20, 25}
Set of prime numbers between 10 and 40: {11, 13, 17, 19, 23, 29, 31, 37}

Set Builder Form Sets

Set {2, 4, 6, 8, 10, 12} in set builder form: {x | x is an even natural number, 2 ≤ x ≤ 12}
Set {5, 6, 7, 8, 9, 10} in set builder form: {x | 5 ≤ x ≤ 10}
Set {1, 4, 9, 16, 25} in set builder form: {x | x is a perfect square, x ≤ 25}

Types of Sets

Finite sets: Sets with a limited number of elements such as {2, 4, 6, 8, 10, 12}, {5, 6, 7, 8, 9, 10}, {1, 4, 9, 16, 25}
Infinite sets: Sets that go on indefinitely without end; specific examples not provided in the text
Void set: The empty set, containing no elements

Representing Letters in "College"

Set representing A: {A}
Set representing B: {B}
Set representing C: {C}
Set representing D: {D}

Set Operations on Intervals

Given A: {x | 5 < x < 8, x ∈ R} and B: {x | 1 < x < 8, x ∈ R}
Union of A and B (A ∪ B): {x | 1 < x < 8, x ∈ R}
Intersection of A and B (A ∩ B): {x | 5 < x < 8, x ∈ R}
Difference A - B: {x | 5 < x < 8, x ∈ R} excluding elements of B

Student Failures in Subjects

Total students: 20
Students failed in MATH: 10
Students failed in CS: 12
Students failed in both subjects: 7
Students failed in MATH only: 10 - 7 = 3
Students failed in CS only: 12 - 7 = 5
Students failed in either MATH or CS: (10 + 12 - 7) = 15
Students failed in either subject but not both: (3 + 5) = 8
Students who did not fail in any subject: 20 - 15 = 5

Description

This quiz covers various aspects of set theory, including roster and set builder forms. Participants will explore finite and infinite sets, as well as operations on intervals. Challenge your understanding of sets, operations, and number classifications with this engaging quiz.