Two Value System Question

[leslie7]

pg 307 2020 edition.

In a question where the variables must go into group 1 or 2.

H1->L1 rule

Its contrapositive would be /L1->/H1
And we can infer: L2->H2

However, des this also infer H2->L2? or is it possible to have H in 2 and L in 1 If H2->L2 cannot be inferred?

thank you !

[KelseyWoods]

Hi Leslie!

So the rule and the contrapositive that we have is this:

H1 L1
L2 H2

With conditional reasoning, only the sufficient condition (at the beginning of the arrow) indicates that something else must be true. So if H is in group 1, we know something else that must be true (L is in group 1). And if L is in group 2, we know something else that must be true (H is in group 2).

But do we know anything else if H is in group 2? Nope! H2 is a necessary condition, at the end of the arrow. If you're at the end of the arrow, there's no where else to go, there's nothing else to know. L could be in either group 1 or group 2 if H is in group 2.

Another way to think of it is this: whenever you have a pair of contrapositives, you cannot have the two sufficient conditions together but you can have the two necessary conditions together. So looking at these two contrapositives, we cannot have H1 and L2 at the same time. But we could have L1 and H2 at the same time.

Hope this helps!

Best,
Kelsey