Question 1176997
Let's break down this logical expression and determine the relationship between `~F → G` and `F v G`.

**Understanding the Symbols**

* `~`: Negation (NOT)
* `→`: Implication (IF...THEN)
* `v`: Disjunction (OR)

**Breaking Down the Expressions**

1.  **`~F → G`** (NOT F implies G)
    * This statement is true in all cases except when `~F` is true and `G` is false.
    * In other words, it's false only when `F` is false and `G` is false.

2.  **`F v G`** (F OR G)
    * This statement is true when either `F` is true, `G` is true, or both are true.
    * It is only false when both `F` and `G` are false.

**Truth Table**

To see the relationship clearly, let's create a truth table:

| F     | G     | ~F    | ~F → G | F v G |
| :---- | :---- | :---- | :----- | :---- |
| True  | True  | False | True   | True  |
| True  | False | False | True   | True  |
| False | True  | True  | True   | True  |
| False | False | True  | False  | False |

**Analysis**

* Notice that the truth values for `~F → G` and `F v G` are identical in all rows of the truth table.

**Conclusion**

Therefore, `~F → G` is logically equivalent to `F v G`. They have the same truth values under all possible combinations of `F` and `G`.