Question

, \&\& is the symbol for the Boolean AND operation, and \(\|\) is the symbol for the Boolean OR operation. What is the truth value of the following Boolean expression… # In C#, \&\& is the symbol for the Boolean AND operation, and \(\|\) is the symbol for the Boolean OR operation. What is the truth value of the following Boolean expressions? a. \((3<=3) \& \&(7>5)\) b. \((3<3) \|(7>5)\) c. \((4<1) \& \&(3>2)\)

Short answer

a. True, b. True, c. False

Step-by-step solution

Analyze the First Expression

The first expression is \((3<=3) \&\& (7>5)\). This can be broken into two parts.- First part: \(3 <= 3\) is a comparison that evaluates if 3 is less than or equal to 3, which is **true** since 3 is equal to 3.- Second part: \(7 > 5\) checks if 7 is greater than 5, which is also **true** because 7 is indeed greater than 5.Since both parts of the AND operation are true, the entire expression evaluates to **true**.

Evaluate the Second Expression

The second expression is \((3<3) \| (7>5)\).- First part: \(3 < 3\) checks if 3 is less than 3. This is **false** because 3 is equal to 3, not less.- Second part: \(7 > 5\) checks if 7 is greater than 5, which is **true**.In an OR operation, the entire expression evaluates to **true** if at least one part is true. So, despite \(3 < 3\) being false, the overall expression results in **true** because \(7>5\) is true.

Calculate the Third Expression

The third expression is \((4<1) \& (3>2)\).- First part: \(4 < 1\) checks if 4 is less than 1, which is **false** since 4 is greater than 1.- Second part: \(3 > 2\) checks if 3 is greater than 2, which is **true** because 3 is indeed greater than 2.In an AND operation, if even one part is false, the whole expression evaluates to false. Therefore, because \(4 < 1\) is false, the entire expression is **false**.

Key concepts

Boolean AND operation

The Boolean AND operation, represented by

• && in C#
• requires both conditions to be true

to return a true value. If any part of the AND operation is false, the overall expression evaluates to false. Think of it as a strict requirement where both criteria must be satisfied.
Imagine you have two conditions:
- "Is the sky blue?"
- "Is it daytime?" For a Boolean AND operation, only if both the sky is blue and it is daytime will the expression return true.
Consider the expression

• (3 <= 3) && (7 > 5)

🙌 This evaluates to true!
Why? Because:
- The first part, (3 <= 3), is true since 3 is equal to 3.
- The second part, (7 > 5), is true since 7 is greater than 5.
Since both parts of the AND condition are true, the entire expression becomes true too. However, if any single condition were false, then no matter how many other truths are present, the result would unfailingly be false. This operation is very unforgiving!

Boolean OR operation

The Boolean OR operation, noted by

• | | in C#
• can be more lenient

compared to AND. In this setup, the entire expression will return true if at least one component is true.
Think of an OR situation like choosing between chocolate or vanilla ice cream. You only need one to feel satisfied, not both!
Look at the expression

• (3 < 3) | | (7 > 5)

💡 It evaluates to true! Why?
- The first part, (3 < 3), is indeed false because 3 isn't less than 3.
- The second part, (7 > 5), is true as 7 is greater than 5.
Even though (3 < 3) is false, the entire expression is true due to the truth of (7 > 5). In this operation, any hint of truth holds immense power, lighting up the whole statement like a beacon!
Underlining the forgiving nature of the OR operation: if one shines, the entire set glows!

Truth value evaluation

Understanding truth value evaluation is like cracking a code to find the ultimate truth or falsehood of a Boolean expression. This involves checking each part of a statement meticulously and then applying the correct logical operation—either AND or OR.
When you're evaluating truth values, the process is to step through each sub-expression one at a time:

• Assess the first component: Determine if it is true or false.
• Move to the next component: Evaluate its truth value.
• Apply the logic operation that binds them: Either AND or OR.

By using the Boolean AND operation:

• All items must be true for the whole to be true.
In contrast, the Boolean OR operation requires only a single ray of truth to validate the expression entirely:
• Just one true value yields a true overall result.
Through careful evaluation of truth values, we unlock the binary magic and seamlessly transition between realms of true and false. Each decision point is pivotal, shaping the course of logical conclusions.