No ai please,

Homework 175 points (5 points each)

Chapter 1.1 - Variables

Fill in the blanks using a variable or variables to rewrite the given statement:

1) Is there a real number whose cube root is the square root of some integer?a) Is there a real number such that _______?b) Does there exist _____ such that _______?

2) Which statement accurately describes the cube root of a negative real number?

a. The cube root of a negative real number is always negative.

b. If a real number is negative, then its cube is negative.

c. For any negative real number, its cube is also negative.

Chapter 1.2 - Sets

1) For each integer , let How many elements are in each of ? Justify your answers.

2) Consider the set T = {}, for some integer i}. What elements are in set T?

Chapter 1.3 - Relations and Functions

1) Let and and define a relation from to as follows: For all , means that is an integer.a) Write as a set of ordered pairs.b) Write the domain and co-domain of .c) Draw and arrow diagram for .

2) Regarding the set {2} and the element 2.a) Is 2 an element of {2}?b) How many elements are in the set {2, 2, 2, 2}? c) How many elements are in the set {0, {0}}? d) Is {0} an element of {{0}, {1}}?e) Is 0 an element of {{0}, {1}}?

Chapter 2.1 - Logical Form and Logical Equivalence

1) Write a truth table for .

2) Determine whether the statements in (a) and (b) are logically equivalent.a) Ben likes both tacos and burritos, and Jen likes tacos but does not like both tacos and burritos.b) It is not the case that both Ben and Jen like tacos and burritos, but it is the case that Jen likes tacos and Ben likes tacos and burritos.

3) Use truth tables to determine whether (p q) (p q) is a tautology or a contradiction.

Chapter 2.2 - Conditional Statements

1) Write a truth table and indicate whether the following statement is true:

2) Use the contrapositive to rewrite the following statement in two ways: "Peter being bitten by a radioactive spider, but not beinginfected by a space parasite, is a necessary condition for being your friendly neighborhood spiderman."

3) Use a truth table to verify the logical equivalence: p (q r) (p q) (p r)

Chapter 2.3 - Valid and Invalid Arguments

1) The Crown Jewels were stolen one evening during an unnecessary gala, but four known thieves were seen in the area and detained for questioning. Inspector Smith questionedthese suspects and determined that all but one of them was lying. He deduced this based on the following statements: Franky: "I'm not a thief! I was just going for a walk, minding my own business when it went down!" Muggsy: "Teddy told me that Paul tried to sell him the jewels, and he wouldn't lie about that!" Paul: "I saw Muggsy with the jewels!" Teddy: "I've never broken any laws and I know Muggsywould never steal anything!" Who stole the Crown Jewels?

Use symbols to write the logical form of each argument for questions 2 and then use a truth table to test the argument for validity. Indicate which columns represent the premises and which represent the conclusion and include a few words of explanation showing that you understand the meaning of validity.

2) Dr Goda is the chair of the IT department or Dr Goda is the chair of the political science department. If Dr Goda is the chair of the IT department, then Dr Goda will be the professor for T INFO 240.

Therefore, Dr. Goda is the chair of the political science department or Dr. Goda will be the professor of T INFO 240.

Use symbols to write the logical form of each argument. If the argument is valid, identify the rule of inference that guarantees its validity. Otherwise, state whether the converse or the inverse error is made.

3) If I go to the movies, I won't finish my homework.

If I don't finish my homework, I won't do well on the midterm.

If I go to the movies, I won't do well on the midterm.