https://r2.erweima.ai/mathbot/image/1721669741214lb8bw5bk.pdf

https://r2.erweima.ai/mathbot/image/1721669741217v7b3ty2b.pdf

It appears there are no direct search results for solving the questions within the documents. Let's review each document individually to identify and solve the questions presented.

I'll start with the first document. Reviewing now.### First Document: Questions and Solutions

The first document appears to be a mathematics exam paper for mature students. Here are the questions and their solutions:

1. **Which of the following is not a subset of the set of counting numbers less than 6?**
   - A. \(\{t, v, w\}\)
   - B. \(\{r, s, t\}\)
   - C. \(\{s, t, v\}\)
   - D. \(\{t, u, v\}\)

   **Solution**: Since the set of counting numbers less than 6 is \(\{1, 2, 3, 4, 5\}\), we need to check which option contains an element not in this set.
   - A, B, C, D all contain elements not in the set \(\{1, 2, 3, 4, 5\}\), as letters are used instead of numbers. Therefore, it seems there is a typo or misprint in the question.

2. **How many subsets has the set \(\{a, b, c, d\}\)?**
   - A. 4
   - B. 8
   - C. 16
   - D. 32

   **Solution**: The number of subsets of a set with \(n\) elements is \(2^n\). For a set with 4 elements, the number of subsets is \(2^4 = 16\).
   - **Answer**: C. 16

3. **How many subsets of the set \(\{a, b, c, d\}\) contain only 1 element?**
   - **Solution**: There are as many single-element subsets as there are elements in the set. For \(\{a, b, c, d\}\), there are 4 such subsets: \(\{a\}\), \(\{b\}\), \(\{c\}\), and \(\{d\}\).
   - **Answer**: 4

4. **If \(A = \{a, b, c, d, e\}\) and \(B = \{c, d, e, f, g\}\), find \(A \cap B\).**
   - A. \(\{c, d, e, f\}\)
   - B. \(\{a, b, c, d\}\)
   - C. \(\{b, c, d, e\}\)
   - D. \(\{c, d, e\}\)

   **Solution**: The intersection of two sets \(A\) and \(B\) is the set of elements that are in both \(A\) and \(B\). Here, \(A \cap B = \{c, d, e\}\).
   - **Answer**: D. \(\{c, d, e\}\)

5. **If \(P = \{x, y, z\}\) and \(Q = \{y, z, a, b\}\), find \(P - Q\).**
   - A. \(\{x, y\}\)
   - B. \(\{x\}\)
   - C. \(\{y, z\}\)
   - D. \(\{a, b\}\)

   **Solution**: The difference of two sets \(P\) and \(Q\) (denoted \(P - Q\)) is the set of elements in \(P\) that are not in \(Q\). Here, \(P - Q = \{x\}\).
   - **Answer**: B. \(\{x\}\)

### Second Document: Questions and Solutions

Let's now review the second document.### Second Document: Questions and Solutions

Here are some of the questions and their solutions from the second document:

1. **Simplify the expression \( 3(x - 2) + 4 \).**
   - **Solution**: 
     \[
     3(x - 2) + 4 = 3x - 6 + 4 = 3x - 2
     \]

2. **If the sum of three consecutive integers is 18, what are the integers?**
   - **Solution**: Let the three consecutive integers be \( x, x+1, x+2 \).
     \[
     x + (x+1) + (x+2) = 18 \\
     3x + 3 = 18 \\
     3x = 15 \\
     x = 5
     \]
     So, the integers are \( 5, 6, 7 \).

3. **Find the value of \( x \) if \( 2x + 3 = 7 \).**
   - **Solution**:
     \[
     2x + 3 = 7 \\
     2x = 4 \\
     x = 2
     \]

4. **Evaluate the expression \( 5^2 - 3^2 \).**
   - **Solution**:
     \[
     5^2 - 3^2 = 25 - 9 = 16
     \]

5. **Solve for \( y \) in the equation \( 4y - 5 = 11 \).**
   - **Solution**:
     \[
     4y - 5 = 11 \\
     4y = 16 \\
     y = 4
     \]

These are some of the questions extracted from the document, along with their solutions. If you have any specific questions or need further details, please let me know.

Do you want details or have any questions about these solutions?

Here are 5 numbered questions for you to ask:
1. Can you solve a specific question from the first document in detail?
2. Can you explain how to find subsets of a given set?
3. What is the intersection of two sets and how is it found?
4. How do you simplify algebraic expressions?
5. Can you show the steps to solve a linear equation?

**Tip:** When solving math problems, always write down each step to avoid mistakes and ensure clarity in your solution process.

Explore detailed solutions to mathematical questions from various documents, covering topics such as set theory, algebraic expressions, and linear equations. Learn about finding subsets of a set, intersection of sets, simplifying algebraic expressions, and solving linear equations step-by-step.

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