Lecture_2 - MA1100 Lecture 2 Elementary Logic Statements...

Info iconThis preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
1 MA1100 Lecture 2 Elementary Logic Statements and Predicates Quantified Statements Negation
Background image of page 1

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

View Full DocumentRight Arrow Icon
MA1100 Lecture 2 2 Mathematical Language ± Not exactly the same as English ± A dialect of English ± Expressing mathematical ideas precisely ± The grammar is Logic Sentences Statements Predicates Others
Background image of page 2
MA1100 Lecture 2 3 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 always lie
Background image of page 3

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

View Full DocumentRight Arrow Icon
MA1100 Lecture 2 4 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
Background image of page 4
MA1100 Lecture 2 5 Predicates A predicate is a (mathematical) sentence that involves variables . With x = 1, y = 1 , 2x + 5y = 7 is true. With x = 3, y = 2 , 2x + 5y = 7 is false. When the variables are substituted with specific values , a predicate becomes a statement . 2x + 5y = 7 is an example of a predicate Example
Background image of page 5

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

View Full DocumentRight Arrow Icon
MA1100 Lecture 2 6 Predicates 1) He thinks MA1100 is an easy module. 2) She says he is cute. He ” is a variable Substitute “ He ”by ±“ The lecturer The lecturer thinks MA1100 is an easy module.
Background image of page 6
MA1100 Lecture 2 7 Predicates 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) When it is clear from the context, we may omit the quantifiers and regard a predicate as a statement.
Background image of page 7

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

View Full DocumentRight Arrow Icon
MA1100 Lecture 2 8 Using the Equal sign = 1) 3 + 4 = 5 + 2 2) 2x + 5y = 7 3) sin 2 θ + cos 2 θ = 1 4) f(x) = x 2 Examples equality equation identity assignment
Background image of page 8
MA1100 Lecture 2 9 Symbolic Representation We denote a statement by capital letters , usually P, Q, R P : 2 is an even number Example means P represents the statement ‘ 2 is an even number Q : 7 is a negative number means Q represents the statement ‘ 7 is a negative number
Background image of page 9

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

View Full DocumentRight Arrow Icon
MA1100 Lecture 2 10 Symbolic Representation P(n) : n is an odd number Q(x,y) : 2x + 5y = 7 Example We denote a predicate by capital letters with the variables involved, such as P(n), Q(x,y), P(2) : 2 is an odd number P(3) : 3 is an odd number
Background image of page 10
MA1100 Lecture 2 11 Quantified Statements There are integers x and y : existential quantifier
Background image of page 11

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

View Full DocumentRight Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/19/2012 for the course SCIENCE MA1100 taught by Professor Forgot during the Fall '08 term at National University of Singapore.

Page1 / 37

Lecture_2 - MA1100 Lecture 2 Elementary Logic Statements...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online