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Can someone please solve them and provide explanation

GAME 1
A music store carries exactly ten types of CDs, both new and used of each of Jazz, opera, pop, rap and soul. The store is having a sale
on some of these types of CDs. The following conditions must apply:
- used pop is on sale; new opera is not
- if both types of pop are on sale, then all soul is
- if both types of jazz are on sale, then no rap is
- if neither type of jazz is on sale, then new pop is
- if either type of rap is on sale, then no soul is

1: which one of the following could be a complete and accurat list of the types of CDs that are on sale?
Answer: used jazz, used pop, new soul, used soul

2: if new soul is not on sale, then which one of the following must be true?
Answer: At leaset one type of pop is not on sale

3: if neither type of jazz is on sale, then each of the following must be true except:
Answer: Used opera is on sale

1.
Go through the rules and eliminate:

A. Wrong: Has a rap CD when both types of Soul are on sale (3rd Rule)
B. Wrong: Has a rap CD on sale alongside a soul CD (5th rule)
C. Wrong: Neither type of Jazz in on sale, but New Pop is no where to be found (4th rule)
D. Wrong: Has both types of pop but only one kind of soul. (2nd rule)
E. Right: Doesn't violate any rules

2. Ok, so no new soul... that means "all soul" won't be on sale, so look for rules where that would be necessary... the 2nd rule says that if both types of pop are on sale then all soul is. So... at least one type of pop isn't on sale, which is answer E. (It would be new pop that isn't on sale obviously)

3. So new and used jazz aren't on sale... well right away we look at the 4th rule (If no jazz, then new pop) so new pop is in. This in turn means that the 2nd rule kicks in (since used pop is always in) and all soul is in as well. Since a soul CD is in, the contrapositive of the 5th rule kicks, so we now know neither rap can be in. So to recap...

We know are on sale: Used Pop, New Pop, Used Soul, New Soul
We know aren't on sale:New Opera, Used Jazz, New Jazz, Used Rap, New Rap
Don't know either way: Used Opera

So the right answer will either by (1) something that cannot be true or (2) something only COULD be true. A refers to Used Opera, which, as we can see, can go either way. Everything else must be true.

Hope this helps.

thank you.