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

Question: Determine if each of the following conditions is True (T) or False (F) given the values of a, b, and c as 2, 4, and 6 respectively. 1. \(a < b\) 2. \(b > c\) 3. \(a + b = c\) 4. \(b - a = c\) 5. \(ac = 2b\) Answer: 1. True (T) 2. False (F) 3. True (T) 4. False (F) 5. False (F)

Step-by-step solution

Condition 1: \(a < b\)

We are given \(a=2\) and \(b=4\). Comparing the two, we observe that \(2 < 4\). Therefore, this condition is True (T).

Condition 2: \(b > c\)

We are given \(b=4\) and \(c=6\). Comparing the two, we observe that \(4\) is not greater than \(6\). Therefore, this condition is False (F).

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

We are given \(a=2, b=4,\) and \(c=6\). Checking if \(a + b = c\), we calculate \(2 + 4 = 6\). Since both sides are equal, this condition is True (T).

Condition 4: \(b - a = c\)

We are given \(a=2, b=4,\) and \(c=6\). Checking if \(b - a = c\), we calculate \(4 - 2 = 2\). Since these values are not equal, this condition is False (F).

Condition 5: \(ac = 2b\)

We are given \(a=2, b=4,\) and \(c=6\). Checking if \(ac = 2b\), we calculate \(2 \times 6 = 12\) and \(2 \times 4 = 8\). Since these values are not equal, this condition is False (F). To summarize the results: 1. \(a < b\) is True (T) 2. \(b > c\) is False (F) 3. \(a + b = c\) is True (T) 4. \(b - a = c\) is False (F) 5. \(ac = 2b\) is False (F)