# truth table

1. Let p, q, and r be the following statements:

p: Sylvia is at the park.

q: Jamie is on the train.

r: Nigel is in the car.

Translate the following statement into English: (~q / p) -> ~r

2. Construct a truth table for ~q -> p.

3. Construct a truth table for (p / ~q) ↔ q.

4. Let p represent the statement, "Jim plays football", and let q represent "Michael plays basketball". Convert the following compound statement into symbols.

Jim does not play football or Michael does not play basketball.

5. Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement.

(p / q) / ~r

6. Determine which, if any, of the three statements are equivalent.

I) If I am hungry, then I will not be able to concentrate at the meeting.

II) Either I am not hungry or I will be able to concentrate at the meeting.

III) If I am able to concentrate at the meeting, then I am not hungry.

7. Identify which argument is invalid.

* Either the panda yawns or she is alert.

The panda did not yawn.

Therefore, she is alert.

* If the panda yawns, then she is not alert.

The panda is not alert.

Therefore, she yawned.

* If Tom is cooking, then I am not hungry.

I am hungry.

Therefore, Tom is not cooking.

* If it is hailing, then I will not go outdoors.

If I will not go outdoors, I will not raise any money for charity.

Therefore, if it is hailing, then I will not raise any money for charity.

* If it is hailing, then I am not going outdoors.

It is hailing.

Therefore, I am not going outdoors.

8. Write the statement in symbols using the p and q given below. Then construct a truth table for the symbolic statement.

p = The doctor prescribed medicine.

q = The patient has recovered.

The doctor did not prescribe medicine but the patient recovered.

#### Solution Preview

1. We read the symbolic notation as "Not q and p implies not r." To translate it into English, we need to figure out the negation of q and r.

q: Jamie is on the train.

So, not q ...

#### Solution Summary

Translate the following statement into English: (~q / p) -> ~r