Symbolizing Compound Conditional Statements in Binary Groupi

[ptraye]

It is easy to symbolize a compound bi-conditional when the variables are separated, as in if John is in then Chris and Robert are out: J --> -C & -R.

On a grouping game I would put (see pdf).

However, how do I diagram a statement for when variables are not separated, as in if Chris and Robert are in, then John is out: C & R --> -J.


From the Manhattan Logic Games archive, Game #34 Easy (Party Problem), I believe I diagrammed the third rule incorrectly: Matt will come to the party, unless both Lance and Reena do.

How would I show this rule on a binary grouping diagram?

[timmydoeslsat]

From the Manhattan Logic Games archive, Game #34 Easy (Party Problem), I believe I diagrammed the third rule incorrectly: Matt will come to the party, unless both Lance and Reena do.

How would I show this rule on a binary grouping diagram?

Very good question!

I want to first say what a biconditional is, which is a word a lot of people use. A biconditional statement can be shown as A<---->B

It is a shortcut for symbolizing a relationship, just as A ---> B symbolizes if A then B.

What you have described above is not a biconditional situation. You do indeed have a compound situation in one of the conditions.

I also want to go over what an unless statement means logically.

A happens unless B happens.

The word "unless" introduces the necessary condition. We will leave this condition in the form it is given to us. What comes before the unless in the statement above is the sufficient condition. We will negate this part. This is what we would have when we diagram it:

~A --->B

We can now think about the same situation but with a compound condition.

A happens unless B and C happen.

~A ---> B and C

[ptraye]

alright. thanks. i was taught a different way of thinking about unless, but it's, basically, the same thing.

[timmydoeslsat]

The most important thing about the word unless is this.

We have a situation occurring the world. It always occurs in the world.

For this situation to not occur in the world, a certain condition must have been met. This is what the word unless is indicating.

A unless B.

A will always occur in the world according to that statement in the absence of B.

So we need to think, what happens if A is not occurring? Well, it must be the case that B is occurring.

[eht1991]

Doesn't "A happens unless B happens" also imply [B ---> ~A]? That is, "if B is happening, then A cannot happen."

The only way this wouldn't make sense would be if you said "A ALWAYS happens unless B happens," which would leave the possibility that if B is happening, A doesn't have to happen, but it could.

Anyone see what I'm saying?

[ManhattanPrepLSAT1]

Doesn't "A happens unless B happens" also imply [B ---> ~A]? That is, "if B is happening, then A cannot happen."

Not exactly. It translates into ~A --> B. "Unless" introduces a necessary condition and implies the negation of the sufficient condition.

The only way this wouldn't make sense would be if you said "A ALWAYS happens unless B happens," which would leave the possibility that if B is happening, A doesn't have to happen, but it could.

Translates into the same thing. ~A --> B No difference here, hope that helps!