Consider the following statements :
1. A = {1, 3, 5} and B = {2,4,7} are equivalent sets.
2. A = {1, 5,9} and B = {1, 5, 5, 9,9} are equal sets.
Which of the above statements is/are correct?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Answer

To determine the correctness of the given statements about sets A and B, we will analyze each statement step by step.

### Step 1: Analyze Statement 1
**Statement 1:** A = {1, 3, 5} and B = {2, 4, 7} are equivalent sets.

**Definition of Equivalent Sets:** Two sets are equivalent if they have the same number of elements, regardless of what those elements are.

- **Count the elements in Set A:**
- Set A has 3 elements: {1, 3, 5}.

- **Count the elements in Set B:**
- Set B has 3 elements: {2, 4, 7}.

Since both sets A and B have the same number of elements (3), we can conclude that they are equivalent sets.

**Conclusion for Statement 1:** This statement is **correct**.

### Step 2: Analyze Statement 2
**Statement 2:** A = {1, 5, 9} and B = {1, 5, 5, 9, 9} are equal sets.

**Definition of Equal Sets:** Two sets are equal if they contain exactly the same elements, counting each element only once.

- **Identify the unique elements in Set A:**
- Set A has unique elements: {1, 5, 9}.

- **Identify the unique elements in Set B:**
- Set B has elements: {1, 5, 5, 9, 9}. However, when we consider unique elements, we only count each element once, resulting in: {1, 5, 9}.

Since both sets A and B contain the same unique elements, we can conclude that they are equal sets.

**Conclusion for Statement 2:** This statement is **correct**.

### Final Conclusion
Both statements are correct.

### Summary:
- Statement 1 is correct (Equivalent sets).
- Statement 2 is correct (Equal sets).

### Final Answer:
Both statements are correct.

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