10 questions · Form 4 Mathematics Bab 3: Operations on Sets
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?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. 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.
2. Given A ⊂ B (A is a subset of B). What is A ∩ B?
Answer: A
If set A is entirely contained within set B (A ⊂ B), all elements of A are in B. Thus, the intersection of A and B is set A itself.
3. Given sets P = {red, blue}, Q = {yellow, blue}, and R = {green, red}. Find P ∩ Q ∩ R.
Answer: D
There is no single color present in all three sets simultaneously. Thus, P ∩ Q ∩ R is the empty set (∅).
4. Given set M = {a, b, c} and set N = {c, d, e}. What is A ∪ B?
Answer: C
The union M ∪ N contains all unique elements present in set M, set N, or both, which gives {a, b, c, d, e}.
5. 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.
6. If set A and set B are disjoint sets (A ∩ B = ∅), what is n(A ∩ B)?
Answer: A
Disjoint sets have no common elements, meaning their intersection is the empty set (∅), so n(A ∩ B) = 0.
7. 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}.
8. Given n(ξ) = 50, n(A) = 28, n(B) = 22, and n(A ∪ B)' = 6. Find n(A ∩ B).
Answer: A
n(A ∪ B) = 50 - 6 = 44. Using n(A ∪ B) = n(A) + n(B) - n(A ∩ B): 44 = 28 + 22 - n(A ∩ B) ⇒ n(A ∩ B) = 50 - 44 = 6.
9. 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.
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}.