{VERSION 2 3 "IBM INTEL NT" "2.3" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "MAPLE ASSIGNMENT 1" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "SET THEOR
Y" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "You \+
can use the following commands to check your understanding of set" }}
{PARA 0 "" 0 "" {TEXT -1 55 "operations. That is, do you agree with Ma
ple's answers?" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "S1:=\{1,2,a,b\};
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "S2:=\{a,1,b,2\};" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "S3:=\{a,x,y,z,17\};" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalb(S1=S2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalb(S1=S3);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 15 "X:=S1 union S3;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "X1:= S1 intersect S3;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "X2:=S1 minus S3;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "X3:=S3 minus S1;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "X2 intersect X3;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "X4:=X1 union X2 union X3;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 22 "evalb(X4=S1 union S3);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 69 "Define a set S4 which has a nonempty intersection with bo
th S1 and S3" }}{PARA 0 "" 0 "" {TEXT -1 61 "but is not a subset of X=
S1 union S3. Test your answer by (i)" }}{PARA 0 "" 0 "" {TEXT -1 9 "co
mputing" }}{PARA 0 "" 0 "" {TEXT -1 67 "S1 intersect S3 intersect S4 a
nd (ii) by using the evalb command to" }}{PARA 0 "" 0 "" {TEXT -1 34 "
show that S4 union X = X is false." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
34 "U:= S1 union S3 union \{3,4,5,b,c\};" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 67 "Calculate the complements of S1, S3, X and X1 with respec
t to the U" }}{PARA 0 "" 0 "" {TEXT -1 58 "above, call them cS1, cS3 e
tc. and use evalb to show that " }}{PARA 0 "" 0 "" {TEXT -1 40 "cS1 un
ion cS3 = c(S1 intersect S3) = cX1" }}{PARA 0 "" 0 "" {TEXT -1 40 "cS1
  intersect cS3 = c(S1 union S3) = cX" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 67 "The other distributive law for sets i
s (A union B) intersect C = (A" }}{PARA 0 "" 0 "" {TEXT -1 69 "interse
ct C) union (B intersect C). Use S1, S3 and S4 as your sets A," }}
{PARA 0 "" 0 "" {TEXT -1 64 "B and C in any order. Calculate the LHS a
nd the RHS of the above" }}{PARA 0 "" 0 "" {TEXT -1 69 "equation and c
ompare the two results to test the law. If you give the" }}{PARA 0 "" 
0 "" {TEXT -1 54 "2 expressions names you can use evalb to test the la
w." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "NUMB
ERS" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "Th
e arithmetic operations are represented in Maple by +, -, *,  / and" }
}{PARA 0 "" 0 "" {TEXT -1 2 "^." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "
a:=(3+4)/5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "b:=(3*4)/5;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "c:=exp(1)^2;" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 65 "For precision of calculation, Mapl
e does not convert fractions or" }}{PARA 0 "" 0 "" {TEXT -1 70 "expres
sions with exponents unless it is forced to by making one of the" }}
{PARA 0 "" 0 "" {TEXT -1 63 "numbers decimal such as replacing 3 by 3.
 or by using the evalf" }}{PARA 0 "" 0 "" {TEXT -1 58 "command.  exp(1
) is Maple's way of inputting the number e." }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "(3.+4)/5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 
"evalf(a);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "evalf(exp(1))
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "evalf(Pi);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "3^(1/3);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 15 "evalf(3^(1/3));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 69 "You can use Maple to check your
 arithmetical skills.  For example use" }}{PARA 0 "" 0 "" {TEXT -1 67 
"+, * and brackets to write an expression involving 3, 4 and 7 which" 
}}{PARA 0 "" 0 "" {TEXT -1 5 "gives" }}{PARA 0 "" 0 "" {TEXT -1 69 "th
e answer 49. Does (3/4)+(5/6) = (3+5)/(4+6)?  Check it out. What is" }
}{PARA 0 "" 0 "" {TEXT -1 54 "an alternative expression for calculatin
g (3/4)*(5/6)?" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 68 "Maple does symbolic calculations as well as numerical cal
culations. " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "(x+y)/(w+z);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "(x/w)+(y/z);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "simplify(\"-\"\");" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 69 "The answer is not zero so the two express
ions were not equal. You can" }}{PARA 0 "" 0 "" {TEXT -1 47 "also use \+
Maple to review the laws of exponents." }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 12 "(x^m)+(x^n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "sim
plify(\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "(x^m)*(x^n);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(\");" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "(x^m)^n;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 12 "simplify(\");" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 63 "Maple doesn't recognize the second law of exponents amd t
ry the" }}{PARA 0 "" 0 "" {TEXT -1 56 "following examples to show that
 Maple can make mistakes." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "(5^(3/
2))^(3/4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "5^((3/2)*(3/4
));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(\");" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "5^(9/8);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 
"" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }