Question about conditional reasoning and contrapositive (LG) Forum

[chefigo_08]

This is from PT 31 (June 2000), Section 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.

My question is about diagramming the contra-positive when there are two elements on both sides of the arrow. For example, with the second clue:

NP and UP ---> NS and US

When deriving the contra-positive of the NS and US part, I understand that it would be:
No NS 'OR' US is on sale

What happens to NP and US? Is it no NP 'AND' UP is not on sale or does the first part also become 'OR' ?

Thanks for your help

[esquirelhomme]

When diagramming the second condition, you have to keep the first condition (that UP is on sale) in mind.
Therefore, when diagrammed, the second condition looks like this: NP -> US & NS
Why did I not diagram UP as part of the second condition? Because it is guaranteed to already be on sale no matter what. So, NP on sale indicates that both NP & UP are on sale.

The contrapositive is: -US or –NS -> -NP

Hope this helps.

[chefigo_08]

Yes. Thank you. I understand that. I am still confused about the third and fifth clues that have two elements on either side of the arrow with 'and' / 'or' in between. How does 'and' and 'or' change in the contrapositive. For example, is the diagram for clue third clue diagrammed as:

NJ 'AND' UJ --> -NR 'AND' -UR
Contrapositive - NR 'OR' UR --> -NR 'OR' -UJ
or is it -NR 'AND' -UJ

Basically what happens to the contrapositive when there is an 'and' or 'or' between two elements on the right hand side of the conditional statement.

Thanks.

[objection_your_honor]

"AND" becomes "OR"

"OR" becomes "AND"

This applies to both sides of the conditional.

[chefigo_08]

That is what I wanted to confirm. Thank you