Mathematics Set Theory Quiz

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