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

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
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Solution

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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:

  1. If \( s = 4 \), then \( 8 = s + 3 \) should be true.
  2. 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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