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Let's analyze the provided statements and classify each as either **True** or **False**:

1. **(a)** If \( A = \{h, u, g, h\} \) and \( B = \{h, u, g\} \), then \( |A| = |B| \).

   - **Explanation**: The set \( A = \{h, u, g, h\} \) includes the element "h" twice, but in sets, duplicate elements are not counted. Therefore, \( A = \{h, u, g\} \), which is identical to set \( B \). Since both sets have the same elements, their cardinalities \( |A| \) and \( |B| \) are equal. 
   - **Answer**: **True**

2. **(b)** \( (-1/5)^{-2} = 25 \).

   - **Explanation**: The expression \( (-1/5)^{-2} \) means taking the reciprocal of \( (-1/5)^2 \). First, squaring \( -1/5 \) gives \( 1/25 \), and taking the reciprocal of \( 1/25 \) results in 25.
   - **Answer**: **True**

3. **(c)** \( \sqrt{a + b} = \sqrt{a} + \sqrt{b} \).

   - **Explanation**: The equation \( \sqrt{a + b} = \sqrt{a} + \sqrt{b} \) is generally false. The square root of a sum is not equal to the sum of the square roots unless both \( a \) and \( b \) are zero, but in general, this equality does not hold.
   - **Answer**: **False**

4. **(d)** The inequality \( x^2 + 1 < 1 \) has no solution.

   - **Explanation**: The inequality \( x^2 + 1 < 1 \) implies that \( x^2 < 0 \). However, since \( x^2 \geq 0 \) for all real numbers \( x \), there is no real solution to this inequality.
   - **Answer**: **True**

Would you like further details on any of these solutions?

### Related Questions:
1. How do you calculate the cardinality of a set?
2. What is the general rule for handling negative exponents?
3. When does the equation \( \sqrt{a + b} = \sqrt{a} + \sqrt{b} \) hold true?
4. How do you solve inequalities involving squares of variables?
5. Can you explain the concept of sets and how duplicates are treated in set theory?

**Tip**: Always double-check if the given elements in a set are distinct, as sets do not count repeated elements.

Classify each of the following as either True or False:

(a) If A = {h, u, g, h} and B = {h, u, g}, then |A| = |B|.
(b) (-1/5)^{-2} = 25.
(c) √(a + b) = √a + √b.
(d) The inequality x^2 + 1 < 1 has no solution.

Analyze and classify mathematical statements related to set theory, exponents, square roots, and inequalities. Understand key concepts such as the cardinality of sets, handling negative exponents, properties of square roots, and solving inequalities. Suitable for high school students.

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