# lecture04 - MA1100 Lecture 4 Logic Statements Open...

This preview shows pages 1–10. Sign up to view the full content.

1 MA1100 Lecture 4 Logic Statements Open sentences Disjunction and conjunction Negation Implication Chartrand: section 2.1 – 2.5

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

View Full Document
Lecture 4 2 Mathematical Language ± Not exactly the same as English ± A dialect of English ± Expressing mathematical ideas precisely ± The grammar is Logic Sentences Statements Open sentences Others
Lecture 4 3 Mathematical Language Example A. 2 divides a 2 only if 2 divides a. B. If 2 does not divide a, then 2 does not divide a 2 . C. 2 divides a if and only if 2 divides a 2 . D. 2 divides a is a necessary condition for 2 to divide a 2 . E. 2 divides a is a sufficient for 2 to divide a 2 . If 2 divides a, then 2 divides a 2 . Which of the following has the same meaning as the above?

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

View Full Document
Lecture 4 4 Statements A statement is a sentence that is either true or false ( but not both ). Examples (daily life) 1) MA1100 lectures are on Tuesday and Friday 2) MA1100’s lecturer is a woman 3) MA1100 is an easy module 4) Is MA1100 lecture conducted in LT27? 5) I am lying now
Lecture 4 5 Statements A statement is a sentence that is either true or false ( but not both ). Examples (Mathematical) 1) 3 + 4 = 8 2) 2x + 5y = 7 3) 2x + 5y = 7 is a linear equation in x and y. 4) There are integers x and y such that 2x + 5y = 7 5) For all integers x and y, 2x + 5y = 7

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

View Full Document
Lecture 4 6 Open sentence (Predicates) An open sentence is a (mathematical) sentence that involves variables . With x = 1, y = 1 : 2x + 5y = 7 becomes 2(1) + 5(1) = 7 which is true. With x = 3, y = 2 : 2x + 5y = 7 becomes 2(3) + 5(2) = 7 which is false. When the variables are substituted with specific values , an open sentence becomes a statement . 2x + 5y = 7 is an example of an open sentence Example
Lecture 4 7 Open sentence 1)He thinks MA1100 is an easy module. 2) She says he is cute. He ” is a variable Example (daily life) She ”and±“ he ” are variables

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

View Full Document
Lecture 4 8 Open sentence 1) n is an odd number 2) p is a prime number 3) xy = yx 4) sin 2 θ + cos 2 θ = 1 More examples (Mathematical)
Lecture 4 9 Symbolic Representation We denote a statement by capital letters , usually P, Q, R P

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 04/15/2010 for the course MATHS MA1101R taught by Professor Vt during the Spring '10 term at National University of Singapore.

### Page1 / 31

lecture04 - MA1100 Lecture 4 Logic Statements Open...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online