Homework

Homework

General:
Before beginning this homework, be sure to read the textbook readings and the module notes.
For additional practice, each homework problem has some ungraded examples and sample problems from the text that you can review, and they directly correspond with your graded homework.Work on those problems if needed, and post your questions to this week’s ungraded discussion forum.
Work within this document for your homework, and be sure to show all steps for arriving at your solution.

Section 2.1 Homework

1) Label each of the following as a statement or as “not a statement.” If you find a statement, give its truth value.
Take the highway.
What time is it?
Winston Churchill was the first president of the United States.

This problem is similar to example 1 and problem 2.1.1.

2) Consider the following two propositions:
p: We can go to Cancun.
q: We can go to Iceland.

Using symbolic notation,

Form the conjunction(^).
Form the disjunction (?).
Write the negation(~) of part a) as a logical statement and as an English sentence.
Write the negation(~) of part b) as a logical statement and as an English sentence.

This problem is similar to examples 3 and 4 and problems 2.1.5 and 2.1.10.

3) Consider the following statement: Every number is less than its square. For example, 5<25 and 7<49. Write thestatement “Every number is less that its square” symbolically by defining a predicate and using a quantifier. This problem is similar to example 8 and problem 2.1.14.

4) Let P(n): 2n = n²

What is P(2) as a statement?
What is P(3) as a statement?
Based off of this, would it be correct to say ?n P(n), ?n P(n), both, or neither? Explain.
This problem is similar to examples 8 and 9 and problems 2.1.20 and 2.1.21.

5) Complete the following two truth tables.

(p?q)?p:
p q p?q ? p
T T
T F
F T
F F
(1) (3) (2)

(p?¦?~q?)?q :
p q (p?~q) ? q
T T
T F
F T
F F
(1) (3) (2)

Review tables 2.1–2.3. This problem is similar to problems 2.1.27 and 2.1.28.

Section 2.2Homework

1) Use the following:

p: It is raining.
q: I stay home today.

Write each of the following statement in terms of p and q using logical connectives. (Note: You may have to use negation, ~, in some instances):

It is not raining implies that I stay home today.
It is raining if I stay home today.
I stay home today if and only if it is raining.
It is raining only if I do not stay home today.
It is raining is a sufficient condition for me to stay home today.
It is raining is a necessary condition for me to stay home today.

This problem is similar to example 1 and problems 2.2.1–2.2.2.

2) Write the contrapositive and the converse of the following statement:

If the post office is open, then it is not a national holiday.

Contrapositive:

Converse:

This problem is similar to example 2 and problems 2.2.3–2.2.4.

3) Complete the truth table for p?q?p .

p?q?p:

Explain how the truth table shows us that p?q?p is a tautology, a contingency, or an absurdity. Also explain how the truth table allows you to descredit the other two possiblities.This problem is similar to problems 2.2.10–2.2.12.

Section 2.3Homework
For problems 1–3, state whether the argument given is valid or not. Write the argument symbolically. For example, of the form (p?q)?~q?~p.

1) If the TV is on sale, I will buy the TV.
The TV is not on sale.
? I will not buy the TV.

2) If the TV is on sale or I can finance it, I will buy the TV.
I cannot finance the TV.
? I will not buy the TV.

3) The TV is not on sale or I will buy it.
The TV is on sale.
? I will buy the TV.

These problems are similar to examples 2–6 and problems 2.3.1–2.3.9.

4) Prove or disprove by counterexample: If n3 is odd, then n is odd.This problem is similar to example 9 and problems 2.3.11–2.3.14.

5) Consider the fact (0.5)²=0.25 and 0.25<0.5

Prove or disprove: For any real number, x² < x.This problem is similar to example 9 and problems 2.3.23–2.3.26.

TAKE ADVANTAGE OF OUR PROMOTIONAL DISCOUNT DISPLAYED ON THE WEBSITE AND GET A DISCOUNT FOR YOUR PAPER NOW!