Question

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

Short answer

A. a < b B. b > c C. c - a = b D. a + b = c Answer: A, C, D

Step-by-step solution

Evaluating each condition

We will evaluate each condition individually by comparing it to the given values of variables a, b, and c. Condition 1: a < b By comparing the given values of a and b (2 and 4), we can determine that a is less than b: 2 < 4 - TRUE Condition 2: b > c By comparing the values of b and c (4 and 6), we can determine that b is not greater than c: 4 > 6 - FALSE Condition 3: c-a = b We can subtract the value of a from c and check if the result equals the value of b: 6 - 2 = 4 - TRUE Condition 4: a+b = c We can add the value of a and b and check if the result equals the value of c: 2 + 4 = 6 - TRUE Based on the evaluation of each condition, we have the following results: Condition 1: a < b - T (True) Condition 2: b > c - F (False) Condition 3: c-a = b - T (True) Condition 4: a+b = c - T (True)

Key concepts

Boolean Logic

To understand how we arrived at the truths of the exercise, let us delve into boolean logic. Boolean logic is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted as T and F or respectively 1 and 0. In programming, boolean logic is essential for making decisions. If a particular condition is true, the program might execute a block of code; otherwise, it may skip that block or execute a different one.

Conditions in a program are evaluated using relational operators like <, >, and ==. When these conditions are checked against actual values, the result is a boolean value - either true or false. For instance, in our exercise, when we compare the variables like 'a < b', we are asking: 'Is a less than b?'. Since 2 is indeed less than 4, the boolean expression evaluates to true.

Comparing Variables

In our exercise, comparing variables is vital to solving the conditions presented. When we compare variables, we are essentially ordering them by their value and checking for equality or inequality. This is done using comparison operators: < (less than), > (greater than), and == (equal to), among others.

Programming languages, including Python, use these comparisons to control the flow of the program. For example, in the statement 'b > c', we are questioning if b is greater than c. With b set as 4 and c as 6, our comparison reveals that the condition is false, because 4 is not greater than 6. Thus, understanding how to compare variables correctly is crucial for programming decisions and logic.

Arithmetic Operations in Programming

Arithmetic operations are elementary yet powerful tools in programming, forming the basis for more complex algorithms. In our exercise, we utilized two arithmetic operations: subtraction and addition. The condition 'c - a = b' incorporates subtraction, where we subtract the value of a (2) from c (6). The result, 4, is then compared to the value of b, and because they are equal, the condition is true.

In another condition, 'a + b = c', addition comes into play. Adding a (2) to b (4) yields 6, which equals the value of c, therefore this condition is also true. These operations are fundamental in programming as they allow us to manipulate and evaluate numerical data, leading to meaningful outcomes based on logical conditions.