QuestionPart I (10 pt., 2 pt. each) Indicate whether each of the following statements is true or false.
1. $|A|=|B|$ where $A=\{1,2,\{3,4\}\}$ and $B=\{a, a,\{a\},\{a, b\}\}$.
2. $\{3,4\} \subseteq A$ where $A=\{1,2,\{3,4\}\}$.
3. $\{3,4\} \in P(A)$ where $A=\{1,2,\{3,4\}\}$ and $P(A)$ is the power set of $A$.
4. $(A \cup \emptyset) \cap \emptyset=A$ where $A$ is a set.
5. $\sum_{i=1}^{10} i=\sum_{j=10}^{20}(j-10)$

Studdy Solution
Determine the truth value of statement 5: $\sum_{i=1}^{10} i = \sum_{j=10}^{20}(j-10)$.
- Calculate $\sum_{i=1}^{10} i = 1 + 2 + \ldots + 10 = \frac{10 \times 11}{2} = 55$. - Calculate $\sum_{j=10}^{20}(j-10) = (10-10) + (11-10) + \ldots + (20-10) = 0 + 1 + \ldots + 10 = \frac{10 \times 11}{2} = 55$.
Both sums equal 55.
Statement 5 is \textbf{True}.
The truth values of the statements are:
1. True
2. False
3. True
4. False
5. True