new formal logic quiz

alas, alas! that is exactly what i tried... let me think:

(P1) A is necessary for B
this means "if not A, then not B"... i visualize this as B<A, where "<" means "contained in"

(P2) B, unless C
this means "if not C, then B"... which equals "if not B, then C"... i visualize this as B and C intersecting each other

(P3) A is sufficient for D
this means "if A then D"... i visualize this as A<D

now...

(Q1) D unless A... this means A can be true while D is false... which is in contradiction with P1

(Q3) C unless D... we can have C true, D false; C true, D true; C true, D false, but not C false and D false... lets see... if not C (C false), by P2, then B... if B, by P1, then A... if A, by P3, then D...

i would now vote for (3) AND (4)... (they are equivalent, arent they?)

Another hint: transform all the premises in a clear and comfortable form, and unite them:

(1) A is necessary for B== If B, then A
(2) B, unless C ======= If not C, then B
(3) A is sufficient for D == If A, then D

So, we see the chain: (2)—(1)—(3): If not C, then B. If B, then A. If A, then D.

Then, formulate the right conclusion in 2 steps.

aargh! im feeling so stupid!
we have B=>A, notC=>B, A=>D... or notC=>B=>A=>D

D unless A? notD=>A false (in fact, notD=>notA)
A unless D? notA=>D false
C unless D? notC=>D... winner!!!!
D unless C? notD=>C... id say this is equivalent to notC=>D... so winner as well, isnt it???

i dont get it stolyar, sorry... so ashamed... i still think answer is (3) AND (4)

If not C, then B. If B, then A. If A, then D.

Step 1: If not C, then D. This equals to...
Step 2: D, unless C.

However, we can transform Step 1: If not D, then C; or C, unless D.

(3) and (4) are the correct answers.

New FLQs coming soon.

great question, thx!