Equivalent statement of the statement ''If `9 gt 10` then `3^(2)=5`'' will be

Options

A. If `3^(2)=5" then "9 gt 10`
B. `9lt 10 and 3^(2) ne5`
C. `9lt10 or 3^(2)=5`
D. None of these

Answer

To find the equivalent statement of the statement "If \(9 > 10\) then \(3^2 = 5\)", we can use the logical equivalence of implications. The implication \(A \implies B\) can be rewritten using the following property:

\[ A \implies B \equiv \neg A \lor B \]

Where:
- \(A\) is the statement "9 > 10"
- \(B\) is the statement "3^2 = 5"

### Step-by-Step Solution:

1. **Identify the statements**:
- Let \(A\) be the statement \(9 > 10\).
- Let \(B\) be the statement \(3^2 = 5\).

2. **Negate statement A**:
- The negation of \(A\) (i.e., \(\neg A\)) is "9 is not greater than 10", which can be written as \(9 \leq 10\).

3. **Rewrite the implication**:
- According to the property of implications, we can rewrite \(A \implies B\) as:
\[ A \implies B \equiv \neg A \lor B \]
Therefore, we have:
\[ 9 > 10 \implies 3^2 = 5 \equiv (9 \leq 10) \lor (3^2 = 5) \]

4. **Final expression**:
- The equivalent statement is:
\[ 9 \leq 10 \lor 3^2 = 5 \]

### Conclusion:
The equivalent statement of "If \(9 > 10\) then \(3^2 = 5\)" is:
\[ 9 \leq 10 \lor 3^2 = 5 \]