Logic Games and the double arrow

[Nadia0702]

Hi PS,

I'm trying to figure out the scenarios when A B turns into A B without it being explicitly stated as A B and B A. Can you please offer some insight into this? I hope my question makes sense.

Thanks!

Nadia

[BethRibet]

Hi Nadia,

Thanks for the question! In general, we know there is a double arrow required when we see language in the stimulus or passage that indicates that the two conditions are mutually dependent. So for instance,

Nadia will sleep well if and only if she works out in the morning.

This tells us that if you do work out, you'll sleep well, and it also tells us that if you do sleep well, it must be true that you worked out. The "if" makes works out in the morning (WO) a sufficient condition. (WO -> SW). The "only if" makes it a necessary condition (SW -> WO).

Therefore, we get our double arrow WO <--> SW.

Hope this helps, write back if not?

Beth

[Nadia0702]

Hi Beth,
Yes this helps - essentially for the double arrow to occur, it must be explicitly stated so. Thanks!

Now for the double not arrow, when it is stated H notG, this always results in the case of H G, correct?

[Dave Killoran]

Hi Nadia,

Yes and yes

Double arrows will result from language like "if and only if," "if and only when," or explicit statements that the arrow goes both ways.

Double-not arrows always follow from the A B form.

Thanks!

[Nadia0702]

Thanks you Dave!

[Nikki Siclunov]

A double-arrow will also result from a statement such as, "Either Anna and Bob both go to the movies, or else neither of them does." This can also be diagrammed as A B, because the double-arrow produces only two possible outcomes (both A and B occur, or else neither A nor B occurs).

Just my 2c.

[Nadia0702]

Makes sense, thanks for your added 2c Nikki!