## Math 1190 - Introduction to Sets and Logic

# Midterm B - Solutions

### Problem 1

- (a)
- (b)
- (c)
- The statements are
- False
- True
- True (as a is an element of A)
- True (as b is an element of B).

### Problem 2

The proposition is a tautology, because the last column of the following
truth table consists 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 3a

### Problem 3b

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 4