I need help translating the following statement to symbolic form:

Question

Tigger bounces on the condition that Tigger is the only one; however, Tigger bounces if and only if Rabbit is annoyed, and Tigger bounces only if it is not raining.

Answer 1

I read through the other answer and believe it contains a mistake, so I'll post a correction.

To translate the given complex statement into symbolic form, we will first identify the simple statements within and assign symbols to them. Then we will use logical operators to represent the relationships between these statements. The simple statements can be identified as:

1. Tigger bounces (B)
2. Tigger is the only one (O)
3. Rabbit is annoyed (A)
4. It is raining (R)

With these components, the statement can be broken down into three parts:

1. "Tigger bounces on the condition that Tigger is the only one" can be represented as O -> B, meaning if Tigger is the only one, then Tigger bounces. (This is where I believe Michael had erred.)
2. "Tigger bounces if and only if Rabbit is annoyed" can be represented as B <-> A, meaning Tigger bounces if and only if Rabbit is annoyed.
3. "Tigger bounces only if it is not raining" can be represented as B -> ~R, meaning if Tigger bounces, then it is not raining.

1 contains the phrase "on the condition," which implies that the condition being described is sufficient for what came before the phrase. So, "A on the condition that B" would be read as B -> A, or if B then A. 2 is pretty self explanatory. 3 contains the phrase "only if." When we read "A only if B," we read it as B being necessary for A to be true; that is, if B is false, then A also has to be false. That relationship is described as A -> B, maintaining the order from the statement "A only if B."

So, now we can put the whole thing together. There is more than one way to do it, but it should look something like this (note that I'm using "^" for "and"):

(O -> B) ^ [(B <-> A) ^ (B -> ~R)]