Math Problem Statement

The image contains a list of C-like programming expressions involving integer and boolean operations. Each expression involves different arithmetic and logical evaluations.

Solution

The image contains a list of C-like programming expressions involving integer and boolean operations. Let's go through each problem and compute the result step by step.

1. Expression

c
int x = 2, y = 5, z = 10; int result = x + y - z / x * y;
  • z / x = 10 / 2 = 5
  • 5 * y = 5 * 5 = 25
  • x + y = 2 + 5 = 7
  • 7 - 25 = -18

Result: -18

2. Expression

c
int result = 10 - 2 + 5 * 3 / 1;
  • 5 * 3 = 15
  • 15 / 1 = 15
  • 10 - 2 = 8
  • 8 + 15 = 23

Result: 23

3. Expression

c
int x = 6; int result = x / 2 + x % 2 * x;
  • x / 2 = 6 / 2 = 3
  • x % 2 = 6 % 2 = 0 (modulus gives remainder)
  • 0 * x = 0 * 6 = 0
  • 3 + 0 = 3

Result: 3

4. Expression

c
int result = 5 + 3 * 2 - 8 / 4;
  • 3 * 2 = 6
  • 8 / 4 = 2
  • 5 + 6 = 11
  • 11 - 2 = 9

Result: 9

5. Expression

c
int a = 4, b = 3; int result = a * b + b / a - a;
  • a * b = 4 * 3 = 12
  • b / a = 3 / 4 = 0 (integer division)
  • 12 + 0 = 12
  • 12 - a = 12 - 4 = 8

Result: 8

6. Expression

c
boolean result = 5 > 3 && 8 < 10;
  • 5 > 3 is true
  • 8 < 10 is true
  • true && true is true

Result: true

7. Expression

c
boolean result = 3 > 3 || 8 > 12.8;
  • 3 > 3 is false
  • 8 > 12.8 is false
  • false || false is false

Result: false

8. Expression

c
boolean result = 10 == 10 && (5 > 6 || 3 <= 3);
  • 10 == 10 is true
  • 5 > 6 is false
  • 3 <= 3 is true
  • false || true is true
  • true && true is true

Result: true

9. Expression

c
boolean result = !(7 == 7 || 3 > 2);
  • 7 == 7 is true
  • 3 > 2 is true
  • true || true is true
  • !true is false

Result: false

10. Expression

c
boolean result = (5 > 3 && 7 == 7) && (2 < 1 || 9 >= 9);
  • 5 > 3 is true
  • 7 == 7 is true
  • true && true is true
  • 2 < 1 is false
  • 9 >= 9 is true
  • false || true is true
  • true && true is true

Result: true


Would you like further clarification or additional details on any of these?

Here are five follow-up questions to deepen your understanding:

  1. How does operator precedence affect the calculation in expression 1?
  2. What happens if you switch from integer to floating-point division in expression 5?
  3. What are the rules of precedence for logical operators like && and ||?
  4. Why does integer division truncate the result in expression 5?
  5. How would the result of expression 8 change if we removed the parentheses around the logical OR condition?

Tip: Always remember that in programming, operator precedence can significantly impact the final result of an expression, so it’s important to use parentheses where necessary to ensure correct evaluation.

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Math Problem Analysis

Mathematical Concepts

Integer Arithmetic
Modulo Operation
Boolean Logic
Operator Precedence

Formulas

Order of operations: parentheses, multiplication, division, modulus, addition, subtraction.
Boolean operators: AND (&&), OR (||), NOT (!).

Theorems

Distributive Property
Modulus Theorem
Boolean Algebra

Suitable Grade Level

Undergraduate Level - Introduction to Programming