SET Practice SET – 1
Set Theory: Level 1
1.
If Set A has 10 members, Set B has 15 members, and they have 5 members in common, how many members are in \( A \cup B \) (A or B)?
Solution (B):
Formula: \( n(A \cup B) = n(A) + n(B) – n(A \cap B) \).
\( n(A \cup B) = 10 + 15 – 5 = 20 \).
2.
In a class of 30 students, 20 like Math and 15 like Science. If 10 like both, how many students like at least one of the subjects?
Solution (C):
\( n(M \cup S) = n(M) + n(S) – n(M \cap S) \).
\( 20 + 15 – 10 = 25 \).
3.
Set X = {1, 2, 3, 4} and Set Y = {3, 4, 5, 6}. What is \( X \cap Y \) (intersection)?
Solution (A):
Intersection contains elements present in BOTH sets.
Common elements are 3 and 4.
4.
Of 50 people, 30 like Tea and 20 like Coffee. If everyone likes at least one, how many like both?
Solution (D):
\( \text{Total} = T + C – \text{Both} \).
\( 50 = 30 + 20 – \text{Both} \).
\( 50 = 50 – \text{Both} \implies \text{Both} = 0 \).
5.
In a group of 100 students, 60 study French. How many study ONLY French if 20 study both French and Spanish?
Solution (B):
Only French = Total French – Both.
\( 60 – 20 = 40 \).
6.
If \( A \subset B \), which of the following is true?
Solution (C):
If A is a subset of B, then all elements of A are in B.
Therefore, the intersection (common elements) is just A itself.
7.
In a group of 40 people, 10 like neither tea nor coffee. If 25 like tea and 15 like coffee, how many like both?
Solution (E):
Total = \( T \cup C + \text{Neither} \).
\( 40 = (T \cup C) + 10 \implies T \cup C = 30 \).
\( T \cup C = T + C – \text{Both} \).
\( 30 = 25 + 15 – \text{Both} \).
\( 30 = 40 – \text{Both} \implies \text{Both} = 10 \).
8.
If 70% of students passed Math and 60% passed English, and every student passed at least one, what percent passed both?
Solution (A):
\( 100 = 70 + 60 – \text{Both} \).
\( 100 = 130 – \text{Both} \implies \text{Both} = 30\% \).
9.
If Set A and Set B are disjoint, and \( n(A)=5, n(B)=7 \), what is \( n(A \cap B) \)?
Solution (B):
Disjoint sets have no common elements. The intersection is empty (0).
10.
If 40 people like apples, 30 like bananas, and 10 like both, how many like **only** apples?
Solution (D):
Only Apples = Total Apples – Both.
\( 40 – 10 = 30 \).
Score: 0 / 0