Questions: Is the inverse of the following conditional true? If g ≥ 6, then g>6. yes no

Transcript text: Is the inverse of the following conditional true? If $g \geq 6$, then $g>6$. yes no

Solution

Solution Steps

To determine if the inverse of a conditional statement is true, we need to first understand the original statement and then construct its inverse. The original statement is "If $ g \geq 6 $, then $ g > 6 $." The inverse of this statement is "If $ g \leq 6 $, then $ g < 6 $." We will check if this inverse statement is true for all possible values of $ g $.

Step 1: Understanding the Original Statement

The original conditional statement is $ g \geq 6 $ implies $ g > 6 $. This means that for any value of $ g $ that is greater than or equal to 6, it must also be greater than 6.

Step 2: Constructing the Inverse

The inverse of the original statement is $ g \leq 6 $ implies $ g < 6 $. This means that if $ g $ is less than or equal to 6, it should also be less than 6.

Step 3: Evaluating the Inverse

To evaluate the truth of the inverse, we consider the case when $ g = 6 $. Here, $ g \leq 6 $ is true, but $ g < 6 $ is false. Therefore, the inverse statement does not hold true for all values of $ g $.