Title : Oct 8-7:30 AM (Page 1 of 19)
Title : Oct 8-7:31 AM (Page 2 of 19)
Texans who are female, younger than 35, unemployed, and have no children.
Texans who are females under the age of 35 OR who have a job.
Male texans who are unemployed and have no children.
Title : Oct 8-7:33 AM (Page 3 of 19)
Title : Oct 8-7:35 AM (Page 4 of 19)
Title : Oct 8-7:36 AM (Page 5 of 19)
Then use algebra to solve for n(F intersect T) .
78 - 62 = 16
64 - 62 = 2
Title : Oct 8-7:37 AM (Page 6 of 19)
Title : Oct 8-7:39 AM (Page 7 of 19)
a = 5, b =10, c= 18, d = 2, e = 3, f = 4, g = 7, h = 1
Title : Oct 8-10:46 AM (Page 8 of 19)
Title : Oct 8-7:40 AM (Page 9 of 19)
Title : Oct 8-7:46 AM (Page 10 of 19)
e=6
b + e + d + f = 22
a + b + e + d = 40
b=4
h=5
e+f=8
a + d + g = 55
Now either solve by hand (using substitution), or
do rref in the calculator.
Think of this as:
"dog AND NOT cat AND NOT other"
or, using de Morgan's laws as:
"dog" AND NOT("cat" OR "other")
Title : Oct 8-7:47 AM (Page 11 of 19)
Title : Oct 8-7:47 AM (Page 12 of 19)
{ HH, HT, TH, TT}
{H1,H2,H3,H4,H5,H6, T1,T2,T3,T4,T5,T6}
Title : Oct 8-7:49 AM (Page 13 of 19)
Task 1: choose shirts
Task 2: choose pants
Task 3: choose shoes
T 1 , ..., T 6
N 1 , ...,N 6 =21
N1: 12
N2: 5
N3: 7
= choose a lower case consonant (we say y is a consonant always).
Title : Oct 8-7:49 AM (Page 14 of 19)
Bonus example:
How many passwords are possible if a password
must consist of exactly 100 letters, all lower-case,
and repetitions are allowed?
Title : Oct 8-11:06 AM (Page 15 of 19)
314293064158293914832150662667454365342456156474671888678425296904526695061140971728629797
7211428081697598519192769774092119229713411708289024
Title : Oct 8-11:08 AM (Page 16 of 19)
179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558
632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245
490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168
738177180919299881250404026184124858368
Title : Oct 8-11:11 AM (Page 17 of 19)
Title : Oct 8-7:49 AM (Page 18 of 19)
Title : Oct 9-10:57 AM (Page 19 of 19)