Math Problem Statement
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
cint 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
cint result = 10 - 2 + 5 * 3 / 1;
5 * 3 = 15
15 / 1 = 15
10 - 2 = 8
8 + 15 = 23
Result: 23
3. Expression
cint 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
cint result = 5 + 3 * 2 - 8 / 4;
3 * 2 = 6
8 / 4 = 2
5 + 6 = 11
11 - 2 = 9
Result: 9
5. Expression
cint 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
cboolean result = 5 > 3 && 8 < 10;
5 > 3
istrue
8 < 10
istrue
true && true
istrue
Result: true
7. Expression
cboolean result = 3 > 3 || 8 > 12.8;
3 > 3
isfalse
8 > 12.8
isfalse
false || false
isfalse
Result: false
8. Expression
cboolean result = 10 == 10 && (5 > 6 || 3 <= 3);
10 == 10
istrue
5 > 6
isfalse
3 <= 3
istrue
false || true
istrue
true && true
istrue
Result: true
9. Expression
cboolean result = !(7 == 7 || 3 > 2);
7 == 7
istrue
3 > 2
istrue
true || true
istrue
!true
isfalse
Result: false
10. Expression
cboolean result = (5 > 3 && 7 == 7) && (2 < 1 || 9 >= 9);
5 > 3
istrue
7 == 7
istrue
true && true
istrue
2 < 1
isfalse
9 >= 9
istrue
false || true
istrue
true && true
istrue
Result: true
Would you like further clarification or additional details on any of these?
Here are five follow-up questions to deepen your understanding:
- How does operator precedence affect the calculation in expression 1?
- What happens if you switch from integer to floating-point division in expression 5?
- What are the rules of precedence for logical operators like
&&
and||
? - Why does integer division truncate the result in expression 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