Draw a Venn diagram to represent the union and intersection of these sets. ^ See Problem 3.- T h e le tte r s i n th e w o r d s A L G E B R A , G E O M E T R Y , a n d C A L C U L U S a re r e p r e s e n te d
by the sets V= {A, L, G, E, B, R}, W= {G, E, 0, M, T, R, Y }, and X = {C, A, L, U, S},
respectively. - Let E = {x\jc is a p o s itiv e , c o m p o s ite n u m b e r le s s th a n 1 0 }, F = {1, 2, 4, 5 , 6 , 8, 9 } ,
and G = {x|x is a p o s itiv e , e v e n n u m b e r le s s t h a n o r e q u a l t o 1 0 }. - Let L = { A , B , C, 1, 2 , 3 , h o rs e , c o w , p i g } , M = {-1 , 0,1, B, Y, pig, duck, A }, and
N = {C, 3, duck, A }. - Camping Twenty-eight girls went camping. There were two m ain activities: 4/B See Problem 4.
v o lle y b a ll a n d s w im m in g. F o u r t e e n g ir ls w e n t s w im m in g , 5 p a r t ic ip a t e d i n b o t h
a c tiv itie s , a n d 4 g ir ls d i d n e ith e r. H o w m a n y g ir ls o n l y p la y e d v o lle y b a ll? - W inter Sports A ski shop owner surveys 200 people who ski or snowboard. If
196 p e o p le s k i a n d 1 54 p e o p le d o b o t h a c tiv itie s , h o w m a n y p e o p le s n o w b o a r d?
S o lv e e a c h i n e q u a l i t y. W r i t e t h e s o l u t i o n s as e i t h e r t h e u n i o n o r i n t e r s e c t i o n o f See Problem 5.
tw o sets.- 13 * — 5 1 < 14 28. —6 < n + 7 < 21 29. |8w -l|> 7
- 3 < | 5 d + l l | 3 1. 2\x — 7| >28 3 2. | 4. 5 f - 1.5| < 12
@ Apply F in d e a c h u n i o n o r i n t e r s e c t i o n. L e t W = {5,6,7, 8}, X = {3 ,6 ,9 } , Y = { 2 , 3 , 7 , 8 } ,
andZ= {x|x is a n e v e n w h o le n u m b e r le s s t h a n 1 0 }.
- WUYUZ 34. AflFflZ 35. Wfixnz
- Writing Let M = {jc| x is a m u ltip le o f 3 } a n d N = {x| x is a m u ltip le o f 5 }. D e sc rib e
th e in te rs e c tio n o f M and N. - Think About a Plan B lo o d t y p e is d e t e r m in e d p a r t l y b y w h ic h antigens a re d
b lo o d c e ll h a s. A n a n t ig e n is a p r o t e i n o n th e s u r fa c e o f a r e d b l o o d c e ll. T y p e A
c o n t a in s th e A a n tig e n. T y p e B c o n t a in s th e B a n tig e n. T y p e A B c o n t a in s b o t h
A a n d B a n tig e n s. T y p e O d o e s n o t h a v e a n y a n tig e n s. A h o s p it a l h a s 2 5 p a t ie n t s
w i t h th e A a n tig e n , 17 w i t h th e B a n tig e n , 10 w i t h t h e A a n d B a n tig e n s , a n d
3 0 w i t h o u t A o r B a n tig e n s. H o w m a n y p a t ie n t s a re r e p r e s e n te d b y th e d a ta?- H o w c a n a V e n n d ia g r a m h e lp y o u s o lv e t h e p r o b le m?
- W hat strategies can you use to com plete the Venn diagram?
- Sports In a survey o f students about favorite sports, the results in clu d e 22 w ho
lik e t e n n is , 25 w h o lik e f o o t b a ll, 9 w h o lik e t e n n is a n d f o o t b a ll, 17 w h o lik e t e n n is
a n d b a s e b a ll, 2 0 w h o lik e f o o t b a l l a n d b a s e b a ll, 6 w h o lik e a ll t h r e e s p o rts , a n d
4 w h o lik e n o n e o f th e s p o r ts. H o w m a n y s tu d e n ts lik e o n l y t e n n is a n d f o o t b a ll?
H o w m a n y s tu d e n ts lik e o n l y t e n n is a n d b a s e b a ll? H o w m a n y s tu d e n ts lik e o n ly
baseball and football?
@ 39. Reasoning Suppose A and B are sets such th a t A CB. What is true about A f l B?
J L e s s o n 3 - 8 U nions an d Intersection s o f Sets [ 219
cPowerAlgebra.com