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# Mathematics - Mat 1002 - Week 3 - Logic - 11 Questions

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By Day 6, complete and submit your answers to the W3: Assignment 3 Dropbox.

Here are symbols you may need:      U ∩  [ ] COPY AND PASTE!

1. (2 pts) Write the negation for the statement below.

Someone in the family makes bread.

2. (2 pts) Let p, q, and r be the following statements:

p: Mary is on the bus.
q: April is in the car.
r: Stan is at the zoo.

Translate the following statement into English: (p   r)  q

3. (2 pts) Write the following compound statement in symbolic form

Let p: Today is Friday.
q: Tomorrow is not the day to go shopping.
If tomorrow is not the day to go shopping, then today is not Friday.

4. (4 pts) Construct a truth table for  (p  q)

5. (3 pts) Write the converse, inverse, and contrapositive of the following conditional statement

If the sun is shining, then it will not rain.

6. (5 pts) Determine whether the argument is valid or invalid.

A tree has green leaves and the tree produces oxygen.
This tree has green leaves
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 This tree produces oxygen.

7. (4 pts) Use Euler Diagrams to determine whether the following syllogism is valid or invalid.

All golfers have golf carts.
All members of the A club have golf carts.
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 All members of the A club are golfers

8. (4 pts) Determine the truth value of the statement q  [ r  (p  q)] when p is false, q is true, and r is true.

9. (3 pts) Determine the truth value of the following statement:

Rembrandt was a famous painter and all prime numbers are odd.

10. (3 pts) Use De Morgan's Laws to determine whether the two statements are equivalent

 (p  q),  p  q

11. (4 pts) Determine which, if any, of the three statements are equivalent.

a) If today is Monday, then tomorrow is Tuesday.
b) If today is not Monday, then tomorrow is not Tuesday.
c) If tomorrow is not Tuesday, then today is not Monday.