Hi, V.

Look at it this way:

Assume R is in EVERY photo, period.

If this were true, the stated rule could still be true, because R would be in every photo Y is not in.

However, R would also be in every photo containing Y, too. There's no conflict between these two ideas.

I think what you're doing is making an "incorrect negation" of the Rule. Just because No Y -> R doesn't mean that Y -> No R.

Remember, "incorrect negations" and "incorrect reversals" can never be deduced from an In-Then conditional. Only the Contrapositive (which is both a negation AND a reversal) can be accurately deduced.

Hi Amanda,

Thanks for jumping in and for your perspective. It's a nice way to view it definately. My only concern now is this. There's a list of sufficient terms in PS's Bible that enumerates:

IF

When

Every

Whevever

All

Any

People who

In order to

So when I saw the 'every' I immediately jumped on making it into an if/then statment? Was this not right of me for this particular game? In other words, are you implying for me to not have made that statement into an if/then clause? Is my if/then clause correct and its contra too?

Again: NO Y -----> R

Contra: NO R ------> Y

Here are the rules of this game, basically seven friends that can be alone or together in a photograph:

1. Wendy appears in every photograph that Selma appears in.

2. Selma appears in every photograph that Umiko appears in.

3. Raimundo appears in every photograph that Yakiro does not appear in.

4. Neither Ty nor Raimundo appears in any photograph that Wendy appears in.

If you don't mind me asking then, how would you approach this game Amanda H.?

Hey, V.

You were NOT wrong in making the "Every" statement into an If-Then Conditional.

You were right about the If-Then Conditional (No Y -> R), and you were also therefore right about the Contrapositive of the If-Then Conditional (No R -> Y).

(And the word "Every" does in fact denote an I.T.C.)

So yes: No Y -> R, and No R -> Y.

You were ONLY wrong in inferring the Incorrect NEGATION of the original ITC (Y -> No R, R -> No Y). This is apparently why you thought Y and R could never be together.

However, as noted, we cannot assume that the negation or reversal of an ITC is necessarily true. This is why, for all we know, Y and R can peacefully coexist. All we know from the ITC (and the contrapositive) is that if one is NOT there, the other one WILL be. It's also possible that both will appear together.

Look at it this way. It's a presidential campaign. At EVERY campaign, the Vice-President will appear if the President doesn't. (No P -> VP). If the VP doesn't appear, the President will. (No VP -> P). Obviously, you want at least one of the two to appear at every campaign event.

However, does the fact that at LEAST one will appear at every campaign event mean that they cannot BOTH appear? Of course not. They could also both appear together.

In other words, requiring that at least one appears at every event (or in every picture) does not preclude both from appearing at various events (or in various pictures).