Assignments – Set Theory

If P = { 1,3,5,7,9 } and Q = { 2,3,5,7 }. What are P ∪ Q, and P ∩ Q
P = { 1,3,7,5 } and Q = { 3,7,8,9 }. Find the union of two sets P and Q
Find the Union and Intersection of two sets P and Q Where Set P = { -29, -45, -10, -30, -3, -39, 24} and Set Q = { -46, 21 ,-8}
If X = { Multiples of 3 between 1 and 20 }, and Y = { Odd Natural Numbers up to 14 }. Determine the intersection of two given sets X and Y
What is X ∪ Y if X = { -4, 3, 2, 11, -6 } and Y = { 3, 6, 11, -4, 5 } ?
What is A ∪ B if A = { 2, 3, 4 } and B = { 5, 6, 7 } ?
What is X ∩ Y if X = { -4, 3, 2, 11, -6 } and Y = { 3, 6, 11, -4, 5 } ?
What is A ∩ B if A = { 2, 3, 4 } and B = { 5, 6, 7 } ?
Write the following in set notation: a) The set of all x such that x is not equal to -2. b) The set of all r such that r is less than 4. c) The empty set. d) The set containing only the odd numbers between 0 and 10. e) The set of all x such that x≥3.
Draw a Venn diagram for : A ⊂ B, B ⊂ A, (A U B) , (A ∩ B) , (A – B), (B – A), (A – B)’, (B – A)’, (A U B)’ , (A ∩ B) ‘, A’ U B’, A’ ∩ B’
Draw a Venn diagram for : A U (B ∩ C) = (A U B) ∩ (A U C)
Draw a Venn diagram for : A ∩ (B U C) = (A ∩ B) U (A ∩ C)
Draw a Venn diagram for the following sets: A = {1, 2, 3, 4, 8, 9} and B = {1, 3, 4, 6}
Draw a Venn diagram for the following sets: A = { -3, -2, -1, 0} and B = {0, 1, 2, 3}
Draw a Venn diagram for the following sets: A = {1, 3, 5, 7, 9} and B = {0, 2, 4, 6, 8}
Let A and B be two finite sets such that n(A) = 20, n(B) = 28 and n(A ∪ B) = 36, find n(A ∩ B). (12)
Let A and B be two finite sets such that n(A) = 30, n(B) = 18 and n(A ∪ B) = 26, find n(A ∩ B)? (22)
If n(A – B) = 18, n(A ∪ B) = 70 and n(A ∩ B) = 25, then find n(B). (52)
If If n(A – B) = 12, n(A ∪ B) = 45 and n(A ∩ B) = 15, then find n(B)? (33)
In a group of 60 people, 27 like cold drinks and 42 like hot drinks and each person likes at least one of the two drinks. How many like both coffee and tea? (9)
In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak English only? How many can speak French only and how many can speak both English and French? (57, 28, 15)
In a competition, a school awarded medals in different categories. 36 medals in dance, 12 medals in dramatics and 18 medals in music. If these medals went to a total of 45 persons and only 4 persons got medals in all the three categories, how many received medals in exactly two of these categories? (13)
Each student in a class of 40 plays at least one indoor game chess, carom and scrabble. 18 play chess, 20 play scrabble and 27 play carom. 7 play chess and scrabble, 12 play scrabble and carom and 4 play chess, carom and scrabble. Find the number of students who play (i) chess and carom. (ii) chess, carom but not scrabble. (10, 6)
In a group of 80 people, 37 like cold drinks and 52 like hot drinks and each person likes at least one of the two drinks. Find How many people like both coffee and tea? (9)
In a school, there are 30 teachers who teach Mathematics or Physics. Of these, 18 teach Mathematics and 6 teach both Physics and Mathematics. How many teach Physics only? (12)
In a survey of 80 people, it was found that 35 people read newspaper H, 20 read newspaper T, 15 read the newspaper I, 5 read both H and I, 10 read both H and T, 7 read both T and I, 4 read all three newspapers. Find the number of people who read at least one of the newspapers? (52)
In a school, all pupils play either Hockey or Football or both. 400 play Football, 150 play Hockey, and 130 play both the games. Find (i) The number of pupils who play Football only, (ii) The number of pupils who play Hockey only, (iii) The total number of pupils in the school. (270, 20, 420)
In a survey of university students, 64 had taken mathematics course, 94 had taken chemistry course, 58 had taken physics course, 28 had taken mathematics and physics, 26 had taken mathematics and chemistry, 22 had taken chemistry and physics course, and 14 had taken all the three courses. Find how many had taken one course only. (106)
In a group of students, 65 play foot ball, 45 play hockey, 42 play cricket, 20 play foot ball and hockey, 25 play foot ball and cricket, 15 play hockey and cricket and 8 play all the three games. Find the total number of students in the group (Assume that each student in the group plays at least one game). (100)
In a college, 60 students enrolled in chemistry,40 in physics, 30 in biology, 15 in chemistry and physics,10 in physics and biology, 5 in biology and chemistry. No one enrolled in all the three. Find how many are enrolled in at least one of the subjects. (100)