I did these already, but my professor never uploaded the solutions for these. I

Question

I did these already, but my professor never uploaded the solutions for these. I wanted to make sure I am right.

#1. Several forms of negation are given for each statement. Which are correct if any? Give explanations for full credit – both for correct and incorrect variations.

a. The carton is sealed or the milk is sour.

1. The milk is not sour or the carton is not sealed.

2. The carton is not sealed and also the milk is not sour.

3. If the carton is not sealed, then the milk will be sour.

b. Flowers will bloom only if it rains.

1. The flowers will bloom but it will not rain.

2. The flowers will not bloom and it will not rain.

3. The flowers will not bloom or else it will not rain.

c. If you build it, they will come.

1. If you build it, then they won’t come.

2. You don’t build it, but they do come.

3. You build it, but they don’t come.

Solution:

a:

b:

c:

#2. Construct a truth table for the given compound proposition. Use one column in truth table for exactly one operation.
Remember about order of precedence!!!

qp V pq q’ q

#3. Which rule of inference is used in each argument below?

Alice is a Math major. Therefore, Alice is either a Math major or a CSI major.

Jerry is a Math major and a CSI major. Therefore, Jerry is a Math major.

If it is rainy, then the pool will be closed. It is rainy. Therefore, the pool is closed.

If it snows today, the university will close. The university is not closed today. Therefore, it did not snow today.

If I go swimming, then I will stay in the sun too long. If I stay in the sun too long, then I will sunburn. Therefore, if I go swimming, then I will sunburn.

l go swimming or eat an ice cream. I did not go swimming. Therefore, I eat an ice cream.

TIF FIT FIF

Explanation / Answer

a. The carton is sealed or the milk is sour.
Answer: 2. The carton is not sealed and also the milk is not sour.
Explanation
The carton is sealed : C
The milk is sour: M
The carton is sealed or the milk is sour: C V M
Negation: The carton is sealed or the milk is sour: ~(C V M) = ~C and ~M

b. Flowers will bloom only if it rains.
Answer: 1. The flowers will bloom but it will not rain.
Explanation
Flowers will bloom: B
It rains: R
Flowers will bloom only if it rains: R -> B = ~R V B
Negation: Flowers will bloom only if it rains: ~(~R V B) = R and ~B

c. If you build it, they will come.
Answer: 3. You build it, but they don’t come.
Explanation
You build it: B
They will come: C
If you build it, they will come: B -> C = ~B V C
Negation: If you build it, they will come: ~(~B V C) = B and ~C

Note: One question at a time please -- Policy of Chegg

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