Chapter 4: Problem 23

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

Expert verified

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)

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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

Step by step solution

Condition 1: \(a < b\)

Condition 2: \(c < b\)

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

Condition 4: \(ab = c\)

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

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