Need clarification on logic 'either or' and 'not both'

hjy925soon

Hey, guys. I have some conflicting notes on something and was hoping for some clarification.

/A --> B

and

A ---> /B

are different things, right?

I wrote down:

/A-->B
=Either or; one of A and B must be in, the other is free to float.

A-->/B
=Not both; only one of A and B can be in, the other must be out.

This is what I wrote down from the course but I thought I saw something different in one of the explanations.

TheDeterminedC

I found this logic very confusing at first. I think the best way of understanding it is with an in out game. Lets give it a try.

We have two options to pick from (A and B ). We are able to choose one of each item to be picked, however we like, as long as we follow one rule. If an item is not picked, that item is out.

Rule: A-->/B

/A means A is out, A means A is picked. Alternatively, B means it is picked and /B means B is out.

If the condition is A-->/B (If A is picked, then B is out), we must think back to the CC about when rules trigger and when they fade away. If I tell you A is in, then the sufficient is satisfied and therefore, /B. Or, in other words, B must be out. Now if I tell you /A (A is out), the sufficient condition is negated and the rule falls away. So now that /A is out, with no rule to say what happens next, B could be picked (B) or /A and /B could be out together. This is why this rule is called 'not both'--both A and B cannot be picked simultaneously. Why exactly? Because when A is picked, we know B is out. When B is picked, (contrapositive B-->/A) A must be out. But when we are told one or the other is out, we simply don't have a rule about what must happen next. They turn into a floater!!

Simply change up the conditions and use the same logic. Please let me know if you need further explanation. This concept is absolutely key to becoming fluid with logic. Try and really image why. I am glad you made a post to learn more about how these abstract rules work rather then just memorizing what the terminology is.

TheDeterminedC

I'll just add on and explain the 'or' relationship now with the same in out game.

Rule: /A-->B

If I tell you A is out(/A) then the sufficient condition of our rule kicks and now B must be picked. Alternatively, is B is out (/B) then A must be picked (contrapositive /B-->A). If I told you A is picked, then this negates the sufficient condition and the rule fades away. Where would B go now, is it picked? or is it out? Well, we have no rule anymore so B can go wherever it wants---B can be picked along with A or out by itself.
This is called an 'or' rule because either A or B or both are/is picked. Why exactly? Try and pick them both and see how the rule either forces us to pick one, the other, both, or we will contradict the rule.

Play around with the rule. Really put your focus on the sufficient condition and understand that once a sufficient condition is negated, the rule is no longer in existence! Why would it no longer exist? Lets say A is picked (using the rule from above), then in no world would there ever be an option of it being out because, well, we were just told it is picked!

sillllyxo

What was helpful to me is watching JY's lessons on this like 3 times particularly this one until it clicked - https://7sage.com/lesson/not-both-v-or-truth-tables-longer-explanation/

sillllyxo

it should get to the point that as soon as you see a not both rule like a->/b you automatically know that one of a/b must ALWAYS be out - it's key for in/out games and you notate it on the game board right away.

hjy925soon

@TheDeterminedC said:
I found this logic very confusing at first. I think the best way of understanding it is with an in out game. Lets give it a try.

We have two options to pick from (A and B ). We are able to choose one of each item to be picked, however we like, as long as we follow one rule. If an item is not picked, that item is out.

Rule: A-->/B

/A means A is out, A means A is picked. Alternatively, B means it is picked and /B means B is out.

If the condition is A-->/B (If A is picked, then B is out), we must think back to the CC about when rules trigger and when they fade away. If I tell you A is in, then the sufficient is satisfied and therefore, /B. Or, in other words, B must be out. Now if I tell you /A (A is out), the sufficient condition is negated and the rule falls away. So now that /A is out, with no rule to say what happens next, B could be picked (B) or /A and /B could be out together. This is why this rule is called 'not both'--both A and B cannot be picked simultaneously. Why exactly? Because when A is picked, we know B is out. When B is picked, (contrapositive B-->/A) A must be out. But when we are told one or the other is out, we simply don't have a rule about what must happen next. They turn into a floater!!

Simply change up the conditions and use the same logic. Please let me know if you need further explanation. This concept is absolutely key to becoming fluid with logic. Try and really image why. I am glad you made a post to learn more about how these abstract rules work rather then just memorizing what the terminology is.

You have no idea how much of a breakthrough you provided with your considerate and thorough reply. I took notes on what you laid out for me, and yes, it gave me a deeper understanding. I now know better than to commit to rote memorization. I am still a bit shaky on logic, but I feel like I understand the dynamics now. Thank you so much!

hjy925soon

@sillllyxo said:
What was helpful to me is watching JY's lessons on this like 3 times particularly this one until it clicked - https://7sage.com/lesson/not-both-v-or-truth-tables-longer-explanation/

Thank you for the link. I combed through the CC but did not recognize it before. I will be sure to freshen up on my logic. Have a nice day.

sillllyxo

@hjy925soon said:

@sillllyxo said:
What was helpful to me is watching JY's lessons on this like 3 times particularly this one until it clicked - https://7sage.com/lesson/not-both-v-or-truth-tables-longer-explanation/

Thank you for the link. I combed through the CC but did not recognize it before. I will be sure to freshen up on my logic. Have a nice day.

I didn't either until I looked for it! I hope it helps let me know if you would like further clarification. I am by no means an expert but I feel like I have a pretty good grasp on this.