MATH 215 Discrete Mathematics Worksheets Logic and Proof ...

MATH 215 Discrete Mathematics Worksheets

Logic and Proof

Which of these are propositions? What are the truth values of those that are propositions?

1. Would you like some coffee? 2. I would like coffee with cream and sugar. 3. Either Mom or Dad will pick me up. 4. There is no Chinese or Korean player on this basketball team. 5. What a beautiful day! 6. 3 + 5 = 7. 7. Put on your jacket or you'll catch a cold.

Page 1

MATH 215 Discrete Mathematics Worksheets Build a tree diagram for each of the following Cartesian products.

1. {burger, sandwich} ? {coke, sprite, juice}.

Logic and Proof

2. {burger, sandwich} ? {coke, sprite, juice} ? {fries, chips}.

3. {True, False} ? {True, False} ? {True, False}.

Page 2

MATH 215 Discrete Mathematics Worksheets Evaluate the following.

1. (T F ) F 2. (T ?F ) F

Construct truth tables for the following. 1. ?(p q)

2. (?p) (?q)

Logic and Proof

Page 3

MATH 215 Discrete Mathematics Worksheets

Logic and Proof

Let p, q, and r be the propositions

p : Grizzly bears have been seen in the area. q : Hiking is safe on the trail.

r : Berries are ripe along the trail. Write these propositions using p, q, and r and logical connectives (including negations).

1. Berries are ripe along the trail, but grizzly bears have not been seen in the area.

2. Grizzly bears have not been seen in the area and hiking on the trail is safe, but berries are ripe along the trail.

3. If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area.

4. It is not safe to hike on the trail, but grizzly bears have not been seen in the area and the berries along the trail are ripe.

5. For hiking on the trail to be safe, it is necessary but not sufficient that berries not be ripe along the trail and for grizzly bears not to have been seen in the area.

6. Hiking is not safe on the trail whenever grizzly bears have been seen in the area and berries are ripe along the trail.

Page 4

MATH 215 Discrete Mathematics Worksheets Determine if the following Propositions are logically equivalent.

1. (?p) q and p q.

Logic and Proof

2. (p q) and ?(p q).

3. (p q) r and (p r) (q r).

Page 5

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download