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Schedule: Subject Code:
Set Theory Activity 1
Q.1 . Which of the following are well-defined sets? Put a CHECK mark.
___1. All the colors in the rainbow.
___2. All the honest members of the family.
___3. All the efficient doctors of the hospital.
___4. All the hardworking teachers in a school.
___5. All the prime numbers less than 100.
Q.2. Write the following sets in the set builder form.
1. A = {2, 4, 6, 8}
2. E = {4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, ......., 52}
Q. 3. Write the following sets in the roster form.
1. A = {x : x W, x ≤ 5}
2. B = {x : x I, -3 < x < 3)
3. C = {x : x is divisible by 12}
Q.4. Which of the following are the examples of an empty set? Put a CHECK mark.
___1. The set of even natural numbers divisible by 3.
___2. The set of all prime numbers divisible by 2.
___3. {x : x N, 5 < x < 6}
___4. The set of odd natural numbers divisible by 2.
Q.5. Classify the following as finite and infinite sets. Write F for infinite sets and IN for infinite sets.
___1. The set of days in a week
___2. A = {x : x N x > 1}
___3. B = {x : x is an even prime number}
___4. D = {x : x is a factor of 30}
___5. P = {x : x Z, x < -1}
Q.6 Let A= {x: x is a letter in the word FOLLOW}, B= {y: y is a letter in the word WOLF}
A. A & B are disjoint
B. A=B
C. A B
D. None of these
Q.7. Which of the following are equivalent sets? Put a CHECK mark.
___1. A = {1, 2, 3} B = {4, 5}
___2. P = {q, s, m} Q = {6, 9, 12}
___3. The set of vowels in the English alphabet The set of consonants in the English alphabet
Q.8 . Find the cardinal number of the following sets.
____1. The set of months in a year
____2. The set of letters in the word MATHEMATICS
Q.9 Show the relationship between the following pairs of sets using Venn diagram:
1. X = {letters of English alphabet up to ‘h’}; Y = {all the vowels of English alphabet}
2. A = {even numbers less than 10}; B = {odd numbers less than 10}
3. C = {multiple of 5 less than 30}; D = {multiple of 3 less than 20}
Q.10. . If: A = Set of natural numbers, B = Set of prime numbers and C = Set of even prime numbers
Draw Venn-diagram showing the relationship among the given sets A, B and C.
OPERATIONS ON SETS
Write your answers on the space provided.
I. Find the union of each of the following pairs of sets.
1. A = {2, 4, 6} 2. A = {a, e, i, o, u}
B = {1, 2, 3} B = {a, b, c, d}
II. Find the intersection of each of the following pairs of sets.
3. A = {1, 4, 9, 16} 4. C = {p, q, r, s}
B = {3, 6, 9, 12} D = {a, b}
III. Find the difference of each of the following pairs of sets.
If A = {a, b, c, d} B = {b, c, d, e}
5. A - B 6. B - C
IV. Find the complement.
V.
Let U = {1, 2, 3, 4, 5, 6, 7, 8, A= {1, 2, 5, 7} B = {2, 4, 6, 8}
9}
7. A’ 8. B’
