{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

3 - LECTURE 3 LOGIC(2.1-2.4.when you have eliminated the...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
LECTURE 3: LOGIC ( § 2.1-2.4) ...when you have eliminated the impossible, whatever remains, however improbable, must be the truth. Sir Arthur Conan Doyle (1859 - 1930) 1. Oh say what is truth A statement is a sentence that asserts something that is either true or false (but not both). Example 1. The following are statements: “The sky is blue.” “ π is a real number.” “All dogs are purple.” “The 100th digit of π is 3.” The following are not statements: “Are you happy?” “Give me cake.” “Wow!” We will often use P , Q , and R to denote statements. The truth values are either true (T) or false (F). Example 2. We could let P 1 : 2 = 1 + 1. This is true. We could let P 2 : 3 is even. This is false. Sometimes sentences can depend on variables – we call these open sentences . Example 3. P ( x ) : 3 x = 12 , x Z . This is a true statement, if we plug in x = 4. It is a false statement for any other value of x . We call Z the domain in this case.
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern