lecture04 - MA1100 Lecture 4 Logic Statements Open...

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1 MA1100 Lecture 4 Logic Statements Open sentences Disjunction and conjunction Negation Implication Chartrand: section 2.1 – 2.5
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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
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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?
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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
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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
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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
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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
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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)
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Lecture 4 9 Symbolic Representation We denote a statement by capital letters , usually P, Q, R P
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lecture04 - MA1100 Lecture 4 Logic Statements Open...

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