https://file.aiquickdraw.com/mathbot/file/1729140333678unt1qm6o.jpg

The image provides a table of expressions and answers, with the following variables declared:

- `boolean expr1 = 23 >= 12`, which evaluates to `true` since 23 is greater than or equal to 12.
- `boolean expr2 = 53 <= 45`, which evaluates to `false` since 53 is not less than or equal to 45.
- `int grade = 80`
- `int score = 49`
- `double celsius = 32.22`

Now, let's evaluate each expression:

### a. `expr1 && expr2 || expr1 ^ expr2`
- `expr1 && expr2`: `true && false` = `false`
- `expr1 ^ expr2`: `true ^ false` = `true` (XOR)
- `false || true` = `true`

**Answer: `true`**

---

### b. `(!expr2 != expr2) && expr2 || 15 != 3 * 5`
- `!expr2`: `!false` = `true`
- `!expr2 != expr2`: `true != false` = `true`
- `(true) && expr2`: `true && false` = `false`
- `15 != 3 * 5`: `15 != 15` = `false`
- `false || false` = `false`

**Answer: `false`**

---

### c. `9 != -9 ^ 7 < 9 - 2 && (!expr1 || expr2)`
- `9 != -9`: `true`
- `7 < 9 - 2`: `7 < 7` = `false`
- `9 != -9 ^ false`: `true ^ false` = `true`
- `!expr1`: `!true` = `false`
- `!expr1 || expr2`: `false || false` = `false`
- `true && false` = `false`

**Answer: `false`**

---

### d. `expr1 ^ !expr2 || !true && 23 > 3 * 2`
- `expr1 ^ !expr2`: `true ^ true` = `false`
- `!true`: `false`
- `23 > 3 * 2`: `23 > 6` = `true`
- `false || false && true`: `false || false` = `false`

**Answer: `false`**

---

### e. `expr1 || 34 <= 12 * 3 && (26 > 2 * 12.5)`
- `expr1`: `true`
- `34 <= 12 * 3`: `34 <= 36` = `true`
- `26 > 2 * 12.5`: `26 > 25` = `true`
- `true && true`: `true`
- `true || true` = `true`

**Answer: `true`**

---

### f. `!(expr1 ^ !true) || (expr2 && !false)`
- `!true`: `false`
- `expr1 ^ false`: `true ^ false` = `true`
- `!(true)`: `false`
- `!false`: `true`
- `expr2 && true`: `false && true` = `false`
- `false || false` = `false`

**Answer: `false`**

---

### g. `(celsius >= 26) && (celsius <= 37) ^ true`
- `celsius >= 26`: `32.22 >= 26` = `true`
- `celsius <= 37`: `32.22 <= 37` = `true`
- `true ^ true`: `false`
- `true && false` = `false`

**Answer: `false`**

---

### h. `(score > 50) && (score < 100) || !(true)`
- `score > 50`: `49 > 50` = `false`
- `score < 100`: `49 < 100` = `true`
- `false && true`: `false`
- `!(true)`: `false`
- `false || false` = `false`

**Answer: `false`**

---

### i. `(grade >= 75) && (expr1 || grade < 75)`
- `grade >= 75`: `80 >= 75` = `true`
- `grade < 75`: `80 < 75` = `false`
- `expr1 || false`: `true || false` = `true`
- `true && true` = `true`

**Answer: `true`**

---

### j. `14 * 2 > 28 && expr1 || expr2 ^ (12 > 13)`
- `14 * 2 > 28`: `28 > 28` = `false`
- `expr1`: `true`
- `false && true`: `false`
- `12 > 13`: `false`
- `expr2 ^ false`: `false ^ false` = `false`
- `false || false` = `false`

**Answer: `false`**

---

Would you like more details on any of these steps?

### 5 Follow-up Questions:
1. How does XOR (`^`) work in Boolean logic?
2. Can you explain the difference between logical AND (`&&`) and logical OR (`||`)?
3. Why does the expression `expr1 || true` always evaluate to `true`?
4. In expression (g), why does the result change when using XOR (`^`) with `true`?
5. What is the role of parentheses in expressions to determine the order of operations?

### Tip:
When solving complex Boolean expressions, remember that operations inside parentheses are evaluated first, and the precedence order follows this: `!` (NOT), `^` (XOR), `&&` (AND), then `||` (OR).

Evaluate the Boolean expressions based on the given variable declarations.

Learn how to evaluate Boolean expressions involving logical operators such as AND, OR, NOT, and XOR. The problem includes multiple expressions and variable declarations. Suitable for high school students in Grades 10-12.

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