^ Got It? 3. Let A = { x | x is o n e o f t h e f i r s t f iv e le tte r s i n t h e E n g lis h a l p h a b e t } ,
B= { x | x i s a v o w e l} , a n d C = { x | x i s a le t t e r i n th e w o r d V E G E T A B L E }.
W h ic h le tte r s a re i n a ll t h r e e sets?
You can also use Venn diagram s to show the number o f e le m e n ts i n t h e u n i o n o r
in te rs e c tio n o f sets.Using a Venn Diagram to Show Numbers of Elements
P o llin g O f 5 0 0 c o m m u t e r s p o l l e d , s o m e d r i v e t o w o r k , s o m e t a k e p u b l i c
tra n s p o rta tio n , a n d som e do b o th. T w o h u n d re d co m m u te rs d riv e to w o rk
a n d 1 2 5 u s e b o t h t y p e s o f t r a n s p o r t a t io n. H o w m a n y c o m m u t e r s t a k e
p u b l i c t r a n s p o r t a t io n?- Number who
commute: 500 - Number who drive: 200
- Number who drive
and use public
transportation: 125
Step 1 D r a w a V e n n d ia g r a m. L e t D = com m uters w ho drive
and P = c o m m u t e r s w h o ta k e p u b l i c t r a n s p o r t a t io n.
Step 2 The intersection o f D a n d P r e p r e s e n t s t h e c o m m u t e r s
who use both methods of transportation: DC\P h a s
125 c o m m u te rs.
Step 3 Find the num ber of commuters who only drive:
200 - 125 = 75. E nter 75 in to the V e nn diagram.
Step 4 The total num ber o f com m uters is 500. Subtract to
fin d the n u m b e r o f com m uters w ho use o n ly p u b lic transportatio n:
500 - 200 = 300.
T h e n u m b e r o f c o m m u t e r s u s in g p u b l i c t r a n s p o r t a t io n is 3 0 0 + 125 = 42 5.Go t It? 4. O f 3 0 s tu d e n ts i n s t u d e n t g o v e r n m e n t , 2 0 a re h o n o r s tu d e n ts a n d
9 are o ffic e rs a n d h o n o r s tu d e n ts. A ll o f th e s tu d e n ts are o ffic e rs , h o n o r
s tu d e n ts , o r b o t h. H o w m a n y a re o ffic e r s b u t n o t h o n o r s tu d e n ts?Meed Plan.
Number who. Draw a Venn diagram
use public • Calculate the number of commuters
transportation w h0 only drive- Calculate the number of commuters
who only use public transportation
Pr o b l em
R e c a ll f r o m L e s s o n 3 -6 t h a t t h e g r a p h o f a c o m p o u n d i n e q u a l i t y w i t h t h e w o r d and
contains the overlap o f t h e g r a p h s o f t h e t w o in e q u a lit ie s t h a t f o r m th e c o m p o u n d
in e q u a lity. Y ou can th in k o f th e o ve rla p as th e in te rs e c tio n o f tw o sets. S im ila rly , y o u
c a n t h i n k o f th e s o lu t io n s o f a n or i n e q u a l i t y as t h e u n i o n o f t w o sets.PowerAlgebra.com Lesson 3-8 Unions and Intersections of Sets
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