{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

x1-sample-slides

# x1-sample-slides - Problem 1 Are and logically equivalent...

This preview shows pages 1–5. Sign up to view the full content.

Problem 1. Are ¬ ( ) and ¬ ↔ ¬ logically equivalent? Justify your answer. No. For example if and are both assigned T, then ¬ ( ) is F and ¬ ↔ ¬ is T. In fact ¬ ↔ ¬ is logically equivalent to . So under any assignment of truth values to and these two sentential formulas get opposite truth values. 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem 2. Indicate which of the following assertions of logical equivalence are true and which are false. (a) ( P ( ) Q ( ) ) ≡ ∃ P ( ) ∨ ∃ Q ( ) is true. (b) ( P ( ) Q ( ) ) ≡ ∃ P ( ) ∧ ∃ Q ( ) is false. (c) ( P ( ) Q ( ) ) ≡ ∀ P ( ) → ∀ Q ( ) is false. (d) ( P ( ) Q ( ) ) ≡ ∀ P ( ) ↔ ∀ Q ( ) is false. 2
Problem 3. Let the domain of discourse be the real numbers. Determine whether each of the following is true or false. (a) ∀ ∃ 2 = 2 is true: Let be the same as . (b) ∀ ∃ = 2 is false: If is negative, it has no real square root. (c) ∃ ∀ = 0 is true: Consider = 0. (d) ∀ ∃ + = 1 is true: Let be 1 - . 3

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem 4. Find a formula that is logically equivalent to ¬∀ ∃ ( P ( ) → ∃ R ( ) ) in which any negation symbols immediate precede predicate (relation) sym- bols.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern