Exercise 3

Suppose $P$ and $Q$ are the statements: $P$: Jack passed math. $Q$: Jill passed math.

1. Translate “Jack and Jill both passed math” into symbols.

2. Translate “If Jack passed math, then Jill did not” into symbols.

3. Translate “$P \vee Q$ ” into English.

4. Translate “$\neg(P \wedge Q) \imp Q$ ” into English.

5. Suppose you know that if Jack passed math, then so did Jill. What can you conclude if you know that:

   1. Jill passed math?
   2. Jill did not pass math?