Questions covered in Standard

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. If $A = \{1, 2, \{3, 4\}, 5\}$, which of the following statements is incorrect?
2. If $A = \phi$, then the number of elements in the power set $P(A)$ is
3. The set $\{x : x \in R, -4 < x \le 6\}$ can be written as the interval
4. If $A$ and $B$ are two sets such that $A \subset B$, then $A \cap B$ is equal to
5. In a group of 20 people, 12 like tea and 15 like coffee. If every person likes at least one of the drinks, how many like both?
6. Write the following set in set-builder form: $A = \{1/2, 2/3, 3/4, 4/5, 5/6, 6/7\}$.
7. If $U = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$, $A = \{2, 4, 6, 8\}$ and $B = \{2, 3, 5, 7\}$, find $(A \cup B)'$.
8. Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank spaces:
   (i) $5 \dots A$
   (ii) $8 \dots A$
   (iii) $0 \dots A$
   (iv) $4 \dots A$
9. In a committee, 50 people speak French, 20 speak Spanish and 10 speak both Spanish and French. How many speak at least one of these two languages?
10. Show that for any sets A and B, $A = (A \cap B) \cup (A - B)$.
11. In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers. Find the number of people who read:
    (i) at least one of the newspapers.
    (ii) exactly one newspaper.
12. Case Study: Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set.
    (i) Write the equation relating $m$ and $n$.
    (ii) Find the values of $m$ and $n$.
    (iii) Find the number of proper subsets of the first set.