Expression Evaluation in Data Structures | Operators, Precedence & Boolean Logic Explained!

✅ 1. If Parentheses are Present → Do them first

Parentheses have the highest precedence (Level 1).
They force the enclosed part to be evaluated first — no matter what other operators are outside.

🔹 Example:

✅ 2. If No Parentheses → Use Operator Precedence Rules

🔹 Example:

Now there’s no parentheses, so we follow the default precedence:

• * comes before +
• So: 3 * 2 = 6
• Then: 5 + 6 = 11

✅ Final result: 11

✅ Summary Table

Expression	Evaluated As	Result
(5 + 3) * 2	8 * 2	16
5 + 3 * 2	5 + (3 * 2)	11

if parentheses are there, we always do that part first. If not, we depend on the built-in precedence rules of the operators.

In the group *, /, %, the % operator is called the:

✅ Modulus operator (or modulo operator)

🔹 What does % do?

It gives the remainder after division.

Example:

Explanation:

• 10 / 3 = 3 (quotient)
• 3 * 3 = 9
• 10 - 9 = 1 → this is the remainder

✅ Why if (age > 18 && age < 30) is a Logical Expression

At first, it looks like you’re just comparing numbers:

You’re right that you don’t see true or false written directly.
But actually — the operands here are still Boolean values. They are just results of conditions.

🔹 Let’s analyze it:

Part of Expression	Meaning	Result (if age = 25)
age > 18	Is age greater than 18?	true
age < 30	Is age less than 30?	true
true && true	Logical AND	true

So this:

actually becomes:

Which finally becomes:

✅ Conclusion:

Even though you don’t see true or false written directly, every condition like age > 18 or x == 0 returns a Boolean value (true or false). These values are the operands for the logical operator &&.

So yes — this is a logical expression, and it uses:

• Logical operator: &&
• Boolean operands: the results of age > 18 and age < 30

✅ You are using a logical expression in this while loop:

🔹 Code:

✅ Where is the Logical Expression?

It’s right here:

Even though i < 5 looks like a math comparison, it’s actually a logical condition that returns either:

• true (if i is less than 5), or
• false (if i is 5 or more)

This result (true or false) determines whether the loop continues or stops.

✅ First: What is a Logical Expression?

A logical expression is any expression that returns a Boolean value:

• true ✅
• or false ❌

It can include:

• Logical operators: &&, ||, !
• Comparison operators: <, >, ==, etc.
• Or even just the literal values: true, false

📌 So, a logical expression does not always need to have &&, ||, or !.
As long as the result is true or false, it’s still a logical expression.

✅ Your Example: while (i < 5)

Let’s analyze it:

• i < 5 is a comparison expression
• It checks: “Is i less than 5?”
• The answer is either:
  • true → continue the loop
  • false → stop the loop

💡 That Boolean result makes it a logical expression.

🔎 Comparison vs Logical Operators

Expression	Type	Returns Boolean?	Is Logical Expression?
i < 5	Comparison	✅ Yes	✅ Yes
x == 10	Comparison	✅ Yes	✅ Yes
true && false	Logical operator	✅ Yes	✅ Yes
!true	Logical operator	✅ Yes	✅ Yes
true	Boolean literal	✅ Yes	✅ Yes

🔸 So why is i < 5 a logical expression?

Because:

• It returns a Boolean (true or false)
• It is used in a condition (while, if, etc.)
• That’s the definition of a logical expression

The Boolean condition:

is a logical expression because:

• It uses a comparison operator (<)
• It evaluates to either true or false
• It is often used in control structures like if, while, for, etc.

🔹 Why is it logical?

Because logical expressions are defined as:

Any expression that evaluates to a Boolean value (true or false)

So:

• i < 5 → returns true if i is less than 5, otherwise false
• ✅ Therefore, it’s a logical expression

✅ Why do we call i < 5 a Boolean condition?

Because:

🔹 It returns a Boolean value:

• true ✅ if i is less than 5
• false ❌ if i is 5 or more

📌 So, what is a Boolean condition?

A Boolean condition is:

A statement that checks something and results in true or false