What can you (logically) conclude?

The exercises here test your command of (very) basic logic.

For each short paragraph below, select the answer that best represents what can be concluded. Answers are at the bottom of the page. Don’t peek!

1. “Amir is enrolled in this class. To be enrolled in this class, Amir must either be a math major or an accounting major. But I know he’s not an accounting major.” From this, you can logically conclude that:
a) Amir is a math major.
b) Amir is not a math major.
c) Amir is an accounting major.
d) Nothing can be concluded.

2. “If Betty is at the party, then Carol will not be. And look…Betty is at the party!” From this, you can logically conclude that:
a) Either Betty or Carol will definitely be at the party.
b) Carol is at the party.
c) Carol is not at the party.
d) Nothing can be concluded.

3. “If Betty is at the party, then Carol will not be. And look…Carol is not at the party!” From this, you can logically conclude that:
a) Either Betty or Carol will definitely be at the party.
b) Betty is at the party.
c) Betty is not at the party.
d) Nothing can be concluded.

4. “Either Dave or Enya will be at the party. If Dave is at the party, the party will be fun. If Enya is at the party, the party will be fun.” From this, you can logically conclude that:
a) Dave will see Enya at the party.
b) The party will be fun.
c) The party will not be fun.
d) Nothing can be concluded.

Answers:

  1. a
  2. c
  3. d [Carol’s presence at the party depends on Carol not being there… not the other way around. We don’t know anything about what will determine whether Betty goes or not.]
  4. b