MATH Section 1.1

Identify the expression for the proposition "Getting an A on the final and doing every exercise in this book is sufficient for getting an A in this class" using p, q, and r and logical connectives.

(p ∧ q) → r

Write the given sentence in the "if p, then q" form. That you got the job implies that you had the best credentials.

If you got the job, then you had the best credentials.

Identify the English translation of the compound proposition (p → ¬r) ∨ (q → ¬r).

If you have the flu then you will not pass the course, or if you miss the final exam then you will not pass the course.

Identify an English translation that expresses the compound proposition p → q.

If you have the flu, then you miss the final examination.

Write the given sentence in the "if p, then q" form. If you keep your textbook, it will be a useful reference in your future courses.

If you keep your textbook, then it will be a useful reference in your future courses.

Write the given sentence in the "if p, then q" form. It is necessary to have a valid password to log on to the server.

If you log on to the server, then you have a valid password.

Write the given sentence in the "if p, then q" form. I will remember to send you the address only if you send me an e-mail message.

If you want me to remember to send you the address, then you must send me an email message.

Identify the negation of "Jennifer and Teja are friends."

Jennifer and Teja are not friends.

Which of these are propositions? What are the truth values of those that are propositions? The moon is made of green cheese.

The given statement is a proposition, and the truth value is false.

Which of these are propositions? What are the truth values of those that are propositions? There are no black flies in Maine.

The given statement is a proposition, and the truth value is false.

Which of these are propositions? What are the truth values of those that are propositions? Do not pass go.

The given statement is not a proposition, and the truth value does not exist.

Which of these are propositions? What are the truth values of those that are propositions? 4 + x = 5.

The given statement is not a proposition, and the truth value does not exists.

Identify the negation of "There are 13 items in a baker's dozen." (Check all that apply.)

There are not 13 items in a baker's dozen. The number of items in a baker's dozen is not equal to 13.

Identify the statement that express the compound proposition p ∨ q ∨ r as an English sentence.

You have the flu, or miss the final examination, or pass the course.

Complete the truth table given below for the given proposition. p ⊕ (p ∨ q) .

p | q | (p ∨ q) | p ⊕ (p ∨ q) T | T | T | F T | F | T | F F | T | T | T F | F | F | F

Complete the truth table given below for the given proposition. (p ∧ q) → (p ∨ q).

p | q | p ∧ q | p ∨ q | (p ∧ q) → (p ∨ q) T | T | T | T | T T | F | F | T | T F | T | F | T | T F | F | F | F | T

Complete the truth table given below for the given proposition. (q → ¬p) ↔ (p ↔ q)

p | q | ¬p | q → ¬p | p ↔ q | (q → ¬p) ↔ (p ↔ q) T | T | F | F | T | F T | F | F | T | F | F F | T | T | T | F | F F | F | T | T | T | T

Complete the truth table given below for the given proposition. p → ¬p.

p | ¬p | p → ¬p T | F | F F | T | T

Identify the expression for the proposition "To get an A in this class, it is necessary for you to get an A on the final" using p, q, and r and logical connectives (including negations).

r → p

Identify the expression for the proposition "You get an A in this class, but you do not do every exercise in this book" using p, q, and r and logical connectives (including negations).

r ∧ ¬q