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Let's go through each section of the assignment:

### A. Translate the following verbal phrases into mathematical expressions:

1. **The sum of a number and 12**  
   Mathematical Expression: \( x + 12 \)

2. **Two less than a number**  
   Mathematical Expression: \( x - 2 \)

3. **The quotient of a number and 5**  
   Mathematical Expression: \( \frac{x}{5} \)

4. **Six times a number increased by 11**  
   Mathematical Expression: \( 6x + 11 \)

5. **The difference of a number and three**  
   Mathematical Expression: \( x - 3 \)

6. **Three more than five times a number**  
   Mathematical Expression: \( 5x + 3 \)

7. **A number decreased by 8**  
   Mathematical Expression: \( x - 8 \)

8. **A number divided by 7**  
   Mathematical Expression: \( \frac{x}{7} \)

9. **Three less than twice a number**  
   Mathematical Expression: \( 2x - 3 \)

10. **The product of fifty and twice a number**  
    Mathematical Expression: \( 50 \times 2x = 100x \)

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### B. Translate the following verbal sentences into mathematical sentences:

1. **A number x increased by four is less than ten**  
   Mathematical Sentence: \( x + 4 < 10 \)

2. **The sum of a number and 4 is less than or equal to twice the number**  
   Mathematical Sentence: \( x + 4 \leq 2x \)

3. **Seven times a number diminished by 8 is 20**  
   Mathematical Sentence: \( 7x - 8 = 20 \)

4. **Nine is at most twice a number**  
   Mathematical Sentence: \( 9 \leq 2x \)

5. **The product of 4 and a number increased by 2 is equal to 10**  
   Mathematical Sentence: \( 4x + 2 = 10 \)

6. **Thrice a number decreased by 10 is less than 2 times the number**  
   Mathematical Sentence: \( 3x - 10 < 2x \)

7. **Four times the sum of a number and 5 is greater than 16**  
   Mathematical Sentence: \( 4(x + 5) > 16 \)

8. **The sum of one-fourth of a number and 7 is equal to 19**  
   Mathematical Sentence: \( \frac{x}{4} + 7 = 19 \)

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### C. Perform the indicated operations on the given sets:

Given:
- \( A = \{1, 2, 3\} \)
- \( B = \{

Translate the following verbal phrases into mathematical expressions and sentences, then perform operations on sets.

Learn how to translate verbal phrases into mathematical expressions and sentences. Explore key algebraic concepts like inequalities and set theory operations, including union, intersection, and set difference. Suitable for students in Grades 7-10.

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