Grouping Setup Practice Drill #1

[Billyd87]

Contrapositive Question:

Logic Games Bible 2017 (page 299)

A hiring company must select 3 from a group of 5 (A-E).

Rules
If C is NOT selected, then B is not selected
D and E cannot both be selected
In order for A to be selected, B must be selected

NO C-->NO B

MY QUESTION

How can you logically infer from the NO-C-->NO-B a contrapositive that YESB-->YESC?

I must be hitting a mental wall, but it's going to make me cry. I do not see that logic...

[Adam Tyson]

That's exactly what a contrapositive is, Billy! It's a claim that is logically equivalent to the original conditional claim, but which both reverses the order of the conditions and negates them.

In this case, if C is out, B is also out. That's the rule, and we accept it as true. So, could you have a situation where B is IN and C is OUT? No, because if C was out, then according to the rule, B would have to also be out! That means that if B is in, C must also be in. To do anything else with C would violate that rule.

The language used in this case should also help. The original rule uses the terms "not selected" for both C and B. What happens when we negate "not selected"? We remove the "not" and we just get "selected" - if B is selected, C is selected. Boom, we reversed and negated! That's how contrapositives are made.

This brings up a useful concept for a lot of conditional relationships, especially in Logic Games, and that is the "two value system". That's what you have when there are only two choices available. In an In/Out game like the one described by those rules, there are only two choices - In or Out. There is no third option. When that happens, the negation of a term like "B is Out" can be expressed either using the standard negation (B is NOT out), or, since there is only one other option available, by switching B to that other option (B is IN). This also happens in games that have two groups and every variable is in either one group or else the other, with no third alternative. We also see it come up in a True/False situation in Logical Reasoning, where the negation of "X is True" can be either "X is not true" or else "X is false". There's no third alternative, so negating a condition means moving it to the other option.

Keep playing around with contrapositives, Billy, and remember to reverse AND negate the terms to create a statement that is proven to be true by the original claim because it is the logical equivalent of that claim. Good luck, keep at it!

[Billyd87]

Thank You! I don't really know where exactly it clicked, but it did... I don't even know what I was confused about before.... Thanks a lot. I'll keep working on them!
Your name should be hero.