BiConditional vs When Rule Goes Away

arunima.b12

Hi, I have two questions which might have one simple answer.

1) Can someone please explain to me why I shouldn't do a biconditional every time it says if m, not k (m --> /k). I mean the contrapositive would be if k, not m (k --> /m). So why not write it as m <---> /k ?

2) How does biconditional affect the rule of "if Sufficient condition not satisfied rule goes away and if necessary condition satisfied rule goes away"? when there is "m <---> /k" and the question says "not k" then the rule goes away?

T14plssss

You're confusing biconditional with contrapositive.
Biconditional (M<->/K) would mean both M->/K and /K-> M. But in your conditional /K doesn't imply M.

Here's the two rules you would need for a biconditional:

M->/K | K->/M is the first rule

/K->M | /M->K is the second rule

You combine these rules to form the biconditional
M<-->/K | K<-->/M

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Ex.
Say a passage says:

All Apes are not blue (A->/B) also means if something is blue it's not an ape (B->/A).

So A implies /B, but /B doesn't imply A, so this is not a biconditional because A<->/B isn't true when read from right to left. With this rule something can be not blue and still not be an ape, but no apes can be blue.

It then adds that

The only things that are not blue are apes (/B->A) which also means that if something is not an ape then it is blue (/A->B).

Here we cover the ground missed by the first rule. If something is not blue then it definitely must be an ape. Now we can conclude the biconditional. All apes are not blue, and all not blue things are apes (A->/B)

arunima.b12

Wow I feel dumb for not thinking about it the other way which is if m -->/k is not the same as /k --> m that's illegal reversal. Thank you!