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lecture04&iuml;&frac14;ˆcomplete&iuml;&frac14;‰

# lecture04&iuml;&frac14;ˆcomplete&iuml;&frac...

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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 Announcement Tutorial begin next week Tutorial problems in Intro handouts page 4 Attendance will be taken Homework set 1 due week 4 Homework problems in Intro handouts page 3 (do not mix up tutorial & HW problem sets) Homework format (next slide) Lecture quiz begin next week Finalize your buddy (LQB) today - sign up form Collection of clickers (by next Monday) Mock-up lecture quiz today
Lecture 4 3 Homework format Write on any A4 size paper (double sided) Can be hand-written (no need typing) No need to copy questions, but label the numbering (e.g. 1.12) clearly for each question Write your full name , matric number (Library card number for SM2), and tutorial group (e.g. ST03) clearly on the first page of your homework.

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Lecture 4 4 From last lecture A = {1, 2, 3, 2} B = {1, 2, 3} Are they the same? redundant A = B 9 |A| = 3 9 U c = « ? « Œ U not the same as « œ U always true not always true
Lecture 4 5 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 6 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 condition 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? LQ1
Lecture 4 7 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 A (true) statement A (false) statement Not a statement Not a statement Not a statement LQ2

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LQ3 Lecture 4 8 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 a (false) statement Not a statement a (true) statement a (false) statement x and y are variables a (true) statement
Lecture 4 9 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.

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