Exercise 3.

Suppose \(P\) and \(Q\) are the statements: \(P\text{:}\) Jack passed math. \(Q\text{:}\) 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?

Solution.
in-context