Question

Assume the variables \(a=2, b=4,\) and \(c=6 .\) Circle the \(T\) or \(F\) for each of the following conditions to indicate whether its value is true or false.

Short answer

A) Condition 1: a < b B) Condition 2: c < b C) Condition 3: a + b = c D) Condition 4: ab = c E) Condition 5: (a + b) / c = 1/2 Answer: A) Condition 1 and C) Condition 3 are true, while the rest are false.

Step-by-step solution

Condition 1: \(a < b\)

To determine whether this condition is true or false, we need to compare the values of \(a\) and \(b\). Given that \(a=2\) and \(b=4\), we have: \(2 < 4\), which is true. So the value for condition 1 is True (T).

Condition 2: \(c < b\)

To determine whether this condition is true or false, we need to compare the values of \(c\) and \(b\). Given that \(c=6\) and \(b=4\), we have: \(6 < 4\), which is false. So the value for condition 2 is False (F).

Condition 3: \(a + b = c\)

To determine whether this condition is true or false, we need to add \(a\) and \(b\) and check if the sum is equal to \(c\). Given that \(a=2, b=4, c=6\), we have: \(2 + 4 = 6\), which is true. So the value for condition 3 is True (T).

Condition 4: \(ab = c\)

To determine whether this condition is true or false, we need to multiply \(a\) and \(b\) and check if the product is equal to \(c\). Given that \(a=2, b=4, c=6\), we have: \(2 \times 4 = 6\), which is false as \(2 \times 4 = 8\). So the value for condition 4 is False (F).

Condition 5: \(\frac{a + b}{c} = \frac{1}{2}\)

To determine whether this condition is true or false, we need to add \(a\) and \(b\), divide the sum by \(c\), and check if the result is equal to \(\frac{1}{2}\). Given that \(a=2, b=4, c=6\), we have: \(\frac{2 + 4}{6} = \frac{6}{6} = 1\), which is not equal to \(\frac{1}{2}\). So the value for condition 5 is False (F). In conclusion, we have the following results for each condition: Condition 1: True (T) Condition 2: False (F) Condition 3: True (T) Condition 4: False (F) Condition 5: False (F)

Key concepts

Conditional Statements

Conditional statements are like the decision-makers in programming.
They help the code to choose a path based on different conditions. This is like everyday choices you make, such as deciding what to wear based on the weather.
In programming, a popular conditional statement is the 'if' statement.

• If Statement - Checks if a condition is true. If it is, a certain block of code runs.

Imagine asking, "Is it raining?" If yes, you take an umbrella. In code, this is similar to an "if" statement where we check if a condition holds true to perform an action.
This condition is often a boolean expression that results in either true or false.

Variable Comparison

Variable comparison is a fundamental concept.
It involves checking the relationship between two or more variables. Variables are like containers that hold information, such as numbers or text, that can change over time.When we compare two variables, we look at their values to see how they relate to each other.
Common comparisons include:

• Equal to (==) - Checks if two values are the same.
• Not equal to (!=) - Checks if two values are different.
• Greater than (>) and less than (<) - Checks if one value is larger or smaller than the other.
• Greater than or equal to (>=) and less than or equal to (<=) - Combines equality check with greater or lesser comparison.

Variable comparison allows us to make decisions in code based on the relationships between these values.
For example, in the exercise, the comparison \( a < b \) checks if the value of \( a \) is less than \( b \), making programming logic clear and understandable.

Boolean Expressions

Boolean expressions give us the answers to questions.
They boil complex statements down to either true or false. This concept is pivotal in conditional logic where decisions are based on truth.Each boolean expression evaluates to either true or false.
This clear-cut result helps programmers to create paths and conditions that the code can follow.

• True or False Results - Every boolean expression results in true or false, nothing in between.
• Logical Operators - Such as 'AND', 'OR', and 'NOT' are used to build more complex expressions by combining simpler ones.
  • AND (&&) - Returns true only if both conditions are true.
  • OR (||) - Returns true if at least one condition is true.
  • NOT (!) - Reverses the truth value.

In the provided examples, each condition like \( a < b \) or \( ab = c \) is a boolean expression.
They are used with conditional statements to control the flow of actions in the code.