Questions: Let p and q represent the following simple statements. p: You are human. q: You have gills. Write the following compound statement in symbolic form. You have gills only if you're not human. The compound statement written in symbolic form is.

Let p and q represent the following simple statements.
p: You are human.
q: You have gills.
Write the following compound statement in symbolic form.
You have gills only if you're not human.

The compound statement written in symbolic form is.

Transcript text: Let $p$ and $q$ represent the following simple statements. p : You are human. $q:$ You have gills. Write the following compound statement in symbolic form. You have gills only if you're not human. The compound statement written in symbolic form is $\square$

Solution

Solution Steps

Step 1: Identify the Simple Statements

Let's identify the simple statements involved:

P: You're not human
Q: You have gills

Step 2: Determine the Logical Relationship

The logical relationship based on the given statement ('only if') is: This indicates that 'You have gills' is a necessary condition for 'You're not human'.

Step 3: Translate to Symbolic Form

The symbolic form of the given statement is: Q → P