Math 1002 Week 3 Quiz



Week 3 Assignment 3: Quiz

Please answer the following problems. It is required that you SHOW YOUR WORK step by step to earn full credit.

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.

No one 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

If either Mary is on the bus or Stan is not at the zoo then April is not in the car.

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.

Today is not Friday means ~p, so:

q ( ~p

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

[pic]

The red column is the final answer.

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

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

Converse:

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

Inverse:

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

Contrapositive:

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

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.

P: Tree has green leaves

Q: Tree produces oxygen

The argument is:

P → Q

P

Therefore Q

That’s true.

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

It is INVALID:

[pic]

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.

[pic]

false, true, true = TRUE

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

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

P = Rembrandt was a famous painter

Q = all primes are odd

P is true, Q is not true (2 is prime)

The whole thing is false.

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

( (p ( q), ( p ( (q

No, because De Morgan says:

~(p ^ q) = ~p v ~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.

P: today is Monday

Q: tomorrow is Tuesday

A means p → q

B means ~p → ~q

C means ~q → ~p

A and C are contrapositives so they are equivalent

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