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test 2 review

# test 2 review - x’y’z w(x(yz y’z y’z’ x’yz’...

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Click to edit Master subtitle style 4/21/10 Discrete Mathematics Test 2 Review 2/15/2010

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4/21/10 , {} – ϕ null set { } – ϕ set that contains the null set as an element { , } – 1 2 set that contains 1 and 2 as elements ( , ) – , 1 2 1 and 2 to be taken as separate individual elements Enclosing something in braces changes it from individual elements to a set to be Set Notation Technicalities
4/21/10 One-to-One A B Not one-to- one Is one-to- one

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4/21/10 Prove One-to-One
4/21/10 Find 2 specific values in the domain with the same image OR Prove that the expression isn’t a function Prove not one-to-one

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4/21/10 Onto A B Not one-to- one Is one-to- one
4/21/10 Prove Onto

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4/21/10 Prove not onto
4/21/10 Both one-to-one and onto One-to-one correspondence Bijection A B

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4/21/10 Prove one-to-one Prove onto Prove Bijection
4/21/10 Prove not bijection

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4/21/10 Circuits A A A B B T A A A A A+ B A B F A
4/21/10 wxyz + wxy’z + wxy’z’+wx’yz’+wx’y’z w(xyz + xy’z + xy’z’ + x’yz’ + x’y’z)

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Unformatted text preview: x’y’z) w(x(yz+y’z+y’z’)+x’yz’+xy’z) w(x(yz + y’(z+z’))+x’yz’+xy’z) w(x(yz + y’(1))+x’yz’+xy’z) w(x(yz + y’)+ x’yz’+xy’z) w(xyz + xy’ + x’yz’ + xy’z) w(xy’(1 + z) + xyz + x’yz’) Circuit Simplification y w w w w x x x ’ x x ’ y y ’ y ’ y ’ y z z z z ’ z ’ w x x y ’ y z z 4/21/10 And v.s. Or “And” “Or” ∪ ∨ + A B A B A B 4/21/10 Proving Countability 4/21/10 all integers odd integers integers greater than 7 numbers divisible by .1 reals reals between 0 and 10 Is it Countable? 4/21/10 Big-O Notation 4/21/10 4/21/10 Big O Tricks 4/21/10 N O YE S 4/21/10 Big-O with Logarithms 4/21/10 4/21/10 Modular Arithmetic 4/21/10-17 mod 2 1 144 mod 7 4-101 mod 13 3 199 mod 19 Modular Arithmetic 4/21/10 Modular Arithmetic...
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