MGF 1106 Quiz #2
Name:
~WI" /<Ig
ID# _ _ _ _ _ _ _ _ __
HONOR CODE: On my honor, I have neither given nor received any aid on this
examination.
Signature: ___________________________________
Instructions: Do all scratch work on the test itself. Make sure your final answers
are clearly labelled. Be sure to simplify all answers whenever possible. SHOW
ALL WORK ON THIS QUIZIN ORDER TO RECEIVE FULL CREDIT!!!
No.
1
2
3
4
5
total
Score
/5
/5
/5
/5
/5
/25
1. Let
U=
A=
B =
C=
{1 , 2,3,4,5,a,b,c,d,e} {1,3,5,b,d} {2,3,4,b,c,d} {1,2,a,d,e} Find each of the following sets.
(a) (A n B)'
Af'e--= ~ 3, b, d ~
(All BY :: B-~-(,-"l-,-lf1-5"i -t\-,(-,t,--'J]
(b) Au C' ( , :. ) 3,4/5", b, d} AV c /~ ,"
3, 'i , S"J
~, d ~
(c) (Cn0)'
cn¢::.¢
¢' :::
r-----------~~
~ I, 2., 3, 4/~J 4,1:., c, el, e J
(d) (B' n C')'
Bf -:. f 1,5', Q, t. 3, C' -= 53, ",~) l.,d}
BIn (' -=
fs}
(B/{)C')' =1"'-5-,,-2-,~-,'{-,t,\-,-b,-c.,-d-,t-n
(e) (A n B)
U
B'
AAB-= ~ 'Ib,d}
2. Use t he Venn diagram to represent each set in roster form.
(a) Au G
~ a'~J( , l / ti ,/~ ) j }
(b) B' n G
(c) (A U B )'
~dJjJl}
(d) (B
n G')'
~C
I
CI
(e) An B
)bJ
J, t
I (',
n C'
~ ~ j,
,
I
11
3. A survey of 80 freshmen at MDC was taken to determine what
courses they were taking. Of those surveyed, 36 take math,
32 take English, and 32 take biology. Sixteen take math and
English, 16 take biology and English, and 14 take biology and
math. Six take all three classes.
(a) How many students take math only?
(d-.
(b) How many students take English only?
(c) How many students take biology and English but not math?
(0
(d) How many students do not take biology?
(e) How many students do not take any of t hese three courses?
4. P rove that the following sets are equal. Give as much explana­
tion as possible.
(A' n (B U C) )'
By
DL ~~"""5
L..w/
At&o b ~ ;t~~'5
7
= (A U B') n (A U C')
(A' n(BVC))' :: AU (BUd
u.w) (&vc)' ::
5' f)e ' ,
So
AU(B uc)' -:: AlJ (Bin c') .
By ~ 'D,~+n\,uhw
!..w It v (B' nc,) -= (AU 5') () (tV e) .
J
oR
Bf ~ 1,
/tV~': 1, 'l , Il,S, ~, ~
At f\ (B vc) :: 3, Ca ,1­
(Alf) (PJ.;C))'
=I, 2.J't/ ~ 8
c'-::. I/l, 3, <;
A-uc' :: 1/ 2,3,4, Sl8
Vt-u B')n(Auc t ) = I, 'Z)4,S Ji
5. Express t he following quantified statement in an equivalent way.
Then write its negation and also express its negation in an
equivalent way.
All dogs are not cats.
erVi'/Jw : /Jo &"j5
r\J t.0i
I)A :
tAre Ws .
SO~ dv~ S
Art CQjs .
rl"j WiOll 's e..r vi",A.r: 1k~
Q
V( i b-ls
Cd-.
cJ Iw..l ~ ~
'tl.aJ
IS