CSE20_Lect8(1).pdf

# CSE20_Lect8(1).pdf - CSE 20 DISCRETE MATH Yeonkyung Kim...

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CSE 20 DISCRETE MATH Yeonkyung Kim Clicker frequency: AB Wednesday, April 15, 15

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Midterm 1 4/20 (next Monday) in class. Chap. 1.1-1.3, 3.2-3.4, 2.1 Review lecture slides (Lect1 - Lect 9:review) No cheat sheet or calculator No need to bring a bluebook Yeonkyung Kim: Thursday 10am-12pm at CSE 2116 Ibrahim Awwal: Monday 12pm-2pm & Friday 2pm-3pm at CSE B260A Shaunak Das: Wednesday 5pm-6pm & Thursday 2pm-3pm at AP&M 6434 Soohyun Nam: Thursday 10:30am-11:30am at CSE B260A Kyle Lee: Sunday 3pm-5pm at CSE basement Audrey Lee: Thursday 1pm-3pm at CSE basement Shamim Ahmed: Saturday 3-5pm at CSE basement 2 Wednesday, April 15, 15
Quantifiers G(x,y)= “x > y” Domain = {all real numbers} 3 ( 8 y )( 9 x ) G ( x, y ) For all numbers y, there exists some number x such that x > y. ( 9 x )( 8 y ) G ( x, y ) There exists a number x such that, for all numbers y, x > y. The order of the quantifiers matters. True x may depend on each y False Need to find a common (one, fixed) x such that... Wednesday, April 15, 15

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Quantifiers distributes over 4 9 _ ( 9 x )( P ( x ) _ Q ( x )) , ( 9 x ) P ( x ) _ ( 9 x ) Q ( x ) ( 9 x )( P ( x ) _ Q ( x )) such that P ( x ) is true OR Q ( x ) is true. , For some x , either P ( x ) is true or Q ( x ) is true. , ( 9 x ) P ( x ) _ ( 9 x ) Q ( x ) , There exists some numbers x Wednesday, April 15, 15
Quantifiers distributes over 5 8 ^ ( 8 x )( P ( x ) ^ Q ( x )) , ( 8 x ) P ( x ) ^ ( 8 x ) Q ( x ) ( 8 x )( P ( x ) ^ Q ( x )) , For all x , both P ( x ) and Q ( x ) are true.
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