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Questions and Answers
What is the roster form for the set of integers from -3 to 5?
What is the roster form for the set of integers from -3 to 5?
- {-2, -1, 0, 1, 2, 3, 4, 5}
- {-3, -2, -1, 0, 1, 2, 3, 4}
- {-3, -2, -1, 0, 1, 2, 3, 4, 5} (correct)
- {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6}
Which of the following represents the set of all natural numbers which are multiples of 5 but less than 30 in set builder form?
Which of the following represents the set of all natural numbers which are multiples of 5 but less than 30 in set builder form?
- {x | x > 0, x < 30, x mod 5 = 0}
- {x | 0 < x < 30, x is a natural number, x = 5n for n ∈ N} (correct)
- {x | x < 30, x is natural, x = 5n for n ∈ Z}
- {x | x < 30, x is an integer, x mod 5 = 0}
How many students failed in either MATH or CS but not in both?
How many students failed in either MATH or CS but not in both?
- 10
- 8 (correct)
- 12
- 5
Which of the following sets is a void set?
Which of the following sets is a void set?
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What is the intersection of sets A and B, where A is the interval $(5, x)$ and $x < 8$?
What is the intersection of sets A and B, where A is the interval $(5, x)$ and $x < 8$?
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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
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