## Math 1190 - Introduction to Sets and Logic

# Midterm A - Solutions

### Problem 1

### Problem 2a

### Problem 2b

To receive full credit, it was not necessary to give the intermediate
steps in this problem. A correct final answer was enough. But if you did
include intermediate steps, then I looked at them for partial credit
(positive or negative).

### Problem 3

The proposition is not a tautology, because the last column of the following
truth table does not consist entirely of T's. In grading this question,
I looked at whether you correctly inferred the answer from the truth table.
In other words, to get credit, you had to be consistent with whatever was
given in your truth table.

### Problem 4

- (a)
- (b)
- (c)
- The statements are
- True
- False
- True (as 1is an element of A)
- False (1 isn't even a set, let alone a subset of B).