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:

   \(p\)	\(q\)	\(r \)	\(p \vee (q \wedge r)\)	\((p \rightarrow \neg r) \vee (p\oplus q)\)
   \(\mathrm{T}\)	\(\mathrm{T}\)	\(\mathrm{T}\)
   \(\mathrm{T}\)	\(\mathrm{T}\)	\(\mathrm{F}\)
   \(\mathrm{T}\)	\(\mathrm{F}\)	\(\mathrm{T}\)
   \(\mathrm{T}\)	\(\mathrm{F}\)	\(\mathrm{F}\)
   \(\mathrm{F}\)	\(\mathrm{T}\)	\(\mathrm{T}\)
   \(\mathrm{F}\)	\(\mathrm{T}\)	\(\mathrm{F}\)
   \(\mathrm{F}\)	\(\mathrm{F}\)	\(\mathrm{T}\)
   \(\mathrm{F}\)	\(\mathrm{F}\)	\(\mathrm{F}\)

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