# Homework #1

Due in lecture, Thursday March 7.

You can do homework in a workbook or on separate pieces of paper.

# Questions

1. Draw a truth table for $$(p\wedge q)\vee(p\wedge\neg q)$$. The first two columns should be $$p$$ and $$q$$, as in the examples in lecture. The last column should be $$(p\wedge q)\vee(p\wedge\neg q)$$. Include other columns in the middle as needed.
2. Draw a truth table to show that the inverse and converse of the conditional $$p\rightarrow q$$ are equivalent.
3. In a sentence or two, use facts from lecture (but not a truth table) to convince me that the inverse and converse of $$p\rightarrow q$$ are equivalent. [Hint: statement⇆contrapositive and inverse⇆converse.]
4. Complete this truth table, which uses three propositions and several compound propositions that contain them:
5. With a truth table like the above, show that $$(p\wedge q)\wedge r$$ is equivalent to $$p\wedge (q\wedge r)$$. That is, that order (left to right or right to left) doesn't matter for $$\wedge$$. [The same is true for $$\vee$$.]

# From the Text

Also complete the following questions from the text:

• Section 1.1: 4, 11, 14, 16, 28, 32, 48