Bunuel
Every store on Main Street in Summitville has an awning, and all of these awnings are either green or red.
If the statement above is true, which one of the following must also be true?
I. Some awnings in Summitville are green.
II. If a store in Summitville does not have an awning, then it is not on Main Street.
III. If a store in Summitville has a red awning, then it is on Main Street.
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) I, II, and III
This question is testing conditional statements. You could see something like this in non Math DI questions
Given: If store on Main Street in Summitville, then has an awning.
This is the "If A, then B" structure. So A is a subset of B.
Given: All these awnings (of stores on Main Street in Summitville) are red or green.
I. Some awnings in Summitville are green.Not necessary. We know that all those awnings are red or green. It is possible that all those are red only. The given condition stays true in that case too.
II. If a store in Summitville does not have an awning, then it is not on Main Street.Must be true. This says no awning implies not on Main Street. This is correct. In 'If A, then B' structure, not B implies not A.
Or we can say that if an element is not in the super set B, then it is automatically not in subset A.
III. If a store in Summitville has a red awning, then it is on Main Street.Not necessaruly true. This says that 'B implies A' but that doesn't hold for If structure.
Or we can say that if an element is in the super set B, then it is doesn't imply that it must be in subset A.
Answer (B)Conditionals discussed here:
https://youtu.be/MmlwcTlHZz8https://youtu.be/BW8Ijrhjjq8https://youtu.be/yQYkL1DSslA