Questions: Is the following biconditional true? 8=s+3 if and only if s=4. yes no

Transcript text: Is the following biconditional true? $8=s+3$ if and only if $s=4$. yes no Submit

Solution

Solution Steps

To determine if the biconditional statement "8 = s + 3 if and only if s = 4" is true, we need to check both directions of the implication:

If $ s = 4 $, then $ 8 = s + 3 $ should be true.
If $ 8 = s + 3 $, then $ s = 4 $ should be true.

Step 1: Check if $ s = 4 $ implies $ 8 = s + 3 $

First, we substitute $ s = 4 $ into the equation $ 8 = s + 3 $: \[ 8 = 4 + 3 \] \[ 8 = 7 \] This is false.

Step 2: Check if $ 8 = s + 3 $ implies $ s = 4 $

Next, we solve the equation $ 8 = s + 3 $ for $ s $: \[ 8 = s + 3 \] \[ s = 8 - 3 \] \[ s = 5 \] This does not match $ s = 4 $, so this implication is also false.

Final Answer

\boxed{\text{no}}

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