10 questions · Form 4 Mathematics Bab 3: Operations on Sets
Which set theoretical symbol represents the statement 'element x belongs to both set P and set Q'?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. Which set theoretical symbol represents the statement 'element x belongs to both set P and set Q'?
Answer: B
The intersection symbol ∩ means 'AND', indicating that x belongs to both set P and set Q simultaneously.
2. In a class of 40 students, 25 play football, 20 play badminton, and 8 play both games. How many students do NOT play either game?
Answer: A
Total playing at least one game n(F ∪ B) = 25 + 20 - 8 = 37. Students playing neither = 40 - 37 = 3.
3. Given set A = {2, 3, 5, 7} and set B = {1, 3, 5, 9}. Find A ∩ B.
Answer: A
The intersection A ∩ B consists of elements that are common to both set A and set B. The common elements are 3 and 5.
4. Given set X = {multiples of 3 less than 15} and set Y = {multiples of 5 less than 15}. Find X ∪ Y.
Answer: A
Set X = {3, 6, 9, 12} and Set Y = {5, 10}. The union X ∪ Y combining all elements is {3, 5, 6, 9, 10, 12}.
5. Given A ⊂ B (A is a subset of B). What is A ∪ B?
Answer: B
Since set A is entirely contained within set B, combining all elements of A and B yields set B.
6. If n(A) = 15, n(B) = 20, and n(A ∩ B) = 5, find n(A ∪ B).
Answer: C
Using the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B), we get 15 + 20 - 5 = 30.
7. In a survey of 30 pupils, 18 like Mathematics (M) and 15 like Science (S). If 5 like neither, how many like BOTH Mathematics and Science?
Answer: A
n(M ∪ S) = 30 - 5 = 25 pupils. n(M ∩ S) = n(M) + n(S) - n(M ∪ S) = 18 + 15 - 25 = 8 pupils.
8. Given universal set ξ = {x : x is an integer, 1 ≤ x ≤ 10}, set A = {2, 4, 6, 8, 10}, and set B = {3, 6, 9}. Find (A ∩ B)'.
Answer: B
A ∩ B = {6}. Therefore, (A ∩ B)' includes all elements in ξ except 6, which is {1, 2, 3, 4, 5, 7, 8, 9, 10}.
9. Given ξ = {1, 2, 3, 4, 5, 6, 7}, P = {1, 3, 5}, Q = {2, 3, 4}. Find (P ∪ Q)'.
Answer: C
P ∪ Q = {1, 2, 3, 4, 5}. The complement (P ∪ Q)' consists of remaining elements in ξ, which are {6, 7}.
10. Given sets A = {1, 2, 3}, B = {2, 3, 4}, and C = {3, 4, 5}. Find (A ∩ B) ∪ C.
Answer: A
First, evaluate the brackets: A ∩ B = {2, 3}. Next, take the union with set C: {2, 3} ∪ {3, 4, 5} = {2, 3, 4, 5}.