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 3² = 5", we can follow these steps:

### Step 1: Identify the components of the statement
The given statement is a conditional statement of the form "If P, then Q", where:
- P: 9 > 10
- Q: 3² = 5

### Step 2: Write the equivalent form using logical implications
The equivalent form of the statement "If P, then Q" can be expressed as:
- P → Q (which means "P implies Q")

### Step 3: Use the logical equivalence
Using the logical equivalence, we know that:
- P → Q is equivalent to ¬P ∨ Q
This means "not P or Q".

### Step 4: Determine the negation of P
The negation of P (¬P) is:
- ¬(9 > 10) which simplifies to 9 ≤ 10.

### Step 5: Combine the negation with Q
Now we can combine ¬P with Q:
- ¬P ∨ Q becomes (9 ≤ 10) ∨ (3² = 5).

### Step 6: Write the final equivalent statement
Thus, the equivalent statement of "If 9 > 10, then 3² = 5" is:
- 9 ≤ 10 or 3² = 5.

### Conclusion
The final equivalent statement is:
- "9 ≤ 10 or 3² = 5".