Questions on logical connectives are word problems that require you to read and consolidate information.
You will read several statements that contain logical connectives such as: if . . . then, and/or, each/every, all, some, or none.
You then have to make a logical conclusion based on the information provided.
Logical Connectives − If . . . Then
(1) Use the information below to answer the question that follows.
- A factory grades its products on a scale of 1 to 10 for resale to wholesalers, retailers, and the general public.
- If the product has a grade of 8 to 10, it is classified as “exclusive” and is sold to retailers.
- If the product has a grade of less than 8 but not less than 5, it is classified as “very good” and is sold to the general public.
- If the product has a grade of 4 to 6, it is classified as “good” and is sold to wholesalers.
- If the product has a grade of less than 4, it is not sold but is dismantled for parts.
If a product is graded as 8, which of the following statements could be true?
A. The product will be sold either to retailers or to the general public.
B. The product will be sold to retailers.
C. The product will be sold to wholesalers.
D. The product will be sold to the general public.
E. The product will be dismantled and used for parts.
Read the facts of problems like this one very carefully.
Pay special attention to the logical connectives “if” and “then” in the above statements.
The facts provided in the problem tell us that if the product has a grade of 8 to 10, it is classified as “exclusive” and is sold to retailers.
However, if the grade is less than 8 but not less than 5, it is sold to the general public.
The grade of the product in this problem is exactly 8, so it is sold to retailers.
So, the correct answer is B.
Logical Connectives − Each/Every, All, Some, None
(2) Use the information below to answer the question that follows.
- The soccer team practices every day of each week from Monday to Friday.
- All practices are held from 4:00 to 6:00 pm.
- There will be no practice on the last Friday of the month.
- None of the practices will be held on Saturdays or Sundays.
- Some practices may be canceled during the month of August.
If practice has been canceled for today, which of the following conclusions can be made?
A. It is the last Friday of the month.
B. It is a Saturday or a Sunday.
C. It is a Saturday or Sunday or the last Friday of the month.
D. It is a day in August.
E. The time is 4:00 pm or earlier.
Read the facts and the logical connectives carefully. Also pay special attention to the word “canceled.”
If practice has been canceled for today, we can conclude that it is a day in August.
The facts state that some practices may be canceled during the month of August. This is the only statement that contains the word “canceled.”
As a matter of course, there will be no practices on the last Friday of the month, or on a Saturday or Sunday. However, these practices are not canceled because they never were going to take place.
So, the correct answer is D.