Assignment A
Question 1: In a survey of children who saw three different shows at Walt Disney World, the following information was gathered: 39 children liked The Little Mermaid, 43 children liked 101 Dalmatians, 56 children liked Mickey Mouse, 7 children liked The Little Mermaid and 101 Dalmatians, 10 children liked The Little Mermaid and Mickey Mouse, 16 children liked 101 Dalmatians and Mickey Mouse, 4 children liked The Little Mermaid, 101 Dalmatians, and Mickey Mouse, 6 children did not like any of the shows.
Answer the following questions:
How many students were surveyed?
How many liked The Little Mermaid only?
How many liked 101 Dalmatians only?
How many liked Mickey Mouse only?
Question 2: The table below shows the number of accidents each year at a particular road junction:
a. Work out the mean, median and mode for the values above.
b. A road safety group wants to get the council to make this junction
safer. Which measure will they use to argue for this?
Question 3 Derive the Boolean Expression and construct the switching circuit for the truth table stated
Assignment B
1. Case study:
A survey of faculty and graduate students at the University revealed the following information:
51 admire Moe
49 admire Larry
60 admire Curly
34 admire Moe and Larry
32 admire Larry and Curly
36 admire Moe and Curly
24 admire all three of the Stooges
1 admires none of the Three Stooges
Bases upon the Case Study please answer the following question
Q.No. 
Question 
Option A 
Option B 
Option C 
Option D 

1 
How many people were surveyed? 
83 
82 
84 
81 

2 
How manyadmire Curly,but not Larry nor Moe? 
17 
16 
18 
15 

3 
How manyadmire Larry orCurly? 
77 
78 
30 
31 

4 
How manyadmire exactlyone of the Stooges? 
28 
27 
29 
26 

5 
How manyadmire exactlytwo of the Stooges? 
31 
30 
29 
32 

6 
How manyadmire Larry ? 
49 
45 
47 
42 

7 
How manyadmire all thethree of the stooges? 
26 
24 
30 
40 

8 
How many admire Moe and curly? 
30 
36 
32 
35 

9 
How manyadmire Moe ? 
48 
49 
50 
51 

10 
How manyadmire curly ? 
60 
61 
62 
59 
Assignment C
Q.No. 
Question  Option A  Option B  Option C  Option D 
1  There are 8 students on the curling team and 12students on the badminton team. What is the total number of students on the two teams if three students are on both teams:  20  17  15  14 
2 
IfA={a,{b}} frndP(A) 
{0,{a},{{b}},{{a},{b}}} 
{{a},{{b}},{{a},{b}}} 
{0,{{b}},{{a},{b}}} 
{0,{{b}},{{a},{b}} 
3  Determine the total number of subsets of the following set: {h,i, j, k, 1, m, n}  128  64  32  14 
4  If A= {2,3,4,5,6,7} B={3,5,7,9,11,13} then AB  {2,4,6}  {4,6,7}  {9,11,13}  {3,4,6} 
5  Which output expression might indicate a product ofsums circuit construction? 
A • (B • C) = (A • B) + C 
A+(B + C) = (AB) + (AC)  A • (B + C) = (A • B) + (AC)  (A + B) + C = A + (B + C) 
6  The value that occurs most frequently in a data set is the  Mean  Standard deviation  Mode  Median 
7  Use the union rule toanswer the question.Ifn(A) = 24,n(B) = 69, andn(AUB) = 81; what is n(A PI B)?  36  12  6  14 
8  The number of elements in the power set P(S) of the set S={{0},1,{2,3}}  2  4  8  3 
9  Let U = {q, r, s, t, u, v, w, x, y, z}; A = {q, s, u, w, y}; B= {q,s,y,z} , C= {v,w,x,y,z}and List the members of the indicated set, using set braces (A UB)’  {t,v,x}  {r, t, v, x}  {s, u, w} 
{r, s, t, u, v, w, x, z} 
10  If A and B are two sets, A ∩ B represents:  all elements in either A and B  all elements in both A and B  all elements that arein A but not B  all sets that include A and B 
11 
A non empty set Swhich is closed with a binary operation ‘*’is called group if  The binary operation is associative  There existsidentity elementwith respect to the binary operation.  There exist aunique inverse ofeach element of S with respect to the binary operation  All A, B & C hold. 
12 
There are thirtyfour possible (notisomorphic) graphswith five vertices.Which of thefollowing graphs is isomorphic to its OWN compliment?  The complete graphon five vertices.  The cyclic graph on five vertices.  The path graph on five vertices.  The null graph on five vertices. 
13 
An isomorphism can be proven between a graph T and a graph B if their complements are isomorphic. 
TRUE 
FALSE 
Both a & b  Undetermined 
14 
Which of the
following sets are semigroups? 
The natural numbers with respect to binary operation addition. 
he set of words
over a finite alphabet with the operation v * w =vw of putting thewords together. 
he set of all
subsets of a finite set with theoperation A * B =AUB. 
both a & c 
15 
The power set of an empty set is  null set  singleton set  super set  Power Set 
16 
Let p be “He is tall”and q be “He is handsome “The symbolic form of the
Statement “It is false that he is short or handsome” is 
~(~pVq)  (~pVq)  ~(~P^{A}q)  (~ P ^{A} q ) 
17 
Write the statement in symbols using the p and q given below. . q = The food is good p = I eat too much. If the food is not good, I won’t eat too much. 
~q > ~p  q>~p  q>p  p>~q 
18 
Truth Table:
~(P=>Q)<=>(P^{A}~Q) I believe I am on the right path with the following: P Q P=>Q ~(P=>Q) ~Q P^{A}~Q is 
ttttftftt  fttfff  tffttt  fftftf 
19 
You are given a
binomial randomvariable with n = 25and p = 0.35. The mean for therandom variable is 
8.25 
8.75 
8 
7.85 
20 
Let p represent the statement, “Jim plays football”, and let q represent “Michael plays basketball”. Convert the compound statements into symbols. It is not the case that Jim plays football and Michael does notplay basketball. 
~pAq  ~pA~q  ~(pAq)  ~(pA~q) 
21 
The
Contrapositive of thefollowing implification is> a) If it is hot, then I take a drink. 
If I do not take a drink, then it is not hot.  If it is hot, then Itake a drink.  If I take a drink,then it is hot.  If it is not hot, then I do not take a drink. 
22 
In a normal curve,the line of symmetry for each half of the figure represents which score?  mean  . median  mode  All the above 
23 
given that ( p Vq ) A (~ p V ~ q ) is false, the truth values of p & q are  both false  both true  p true & q false 
p false & q true 
24 
Which of thefollowing is TRUE  The set of all rationalnegative numbersforms a group under multiplication  The set of all non singular matricesforms a groupunder multilication  The set of allmatrices froms agroup under multiplication  Both b & c aretrue 
25 
G{e , a, b ,c} is anabelian group with e as identity element The order of the other elements are  2,2,3  3,3,3  2,2,4  2,3,4 
26 
If the binary operation * is defined on set of ordered pairs of real numbers s ( a,b)8(c,d) =(ad+bc,bd) and is associative ,then(1,2) *(3 ,5) *(3,4)=  (74,40)  (32, 40)  (23, 11)  (7,11) 
27 
Which of the following statement are FALSE  The set of all rationalnumbers is an abelian group under addition  The set of allrational integers isan abelian group under addition  The set of allrational numbersform an abeliangroup under multiplication  None of these 
28 
If a and b arepositive integers.define a* b= a where a .b E O(modulo 7),with this * operation,the inverse of 3 in group G {1,2,3,4,5,6} is 
3 
1 
5 
4 
29 
Let A be non
singular matrices over real numbers and let * be the matrix multiplication operator Then 
A is closed under* but < A, *> is not a semi group 
< A, *> is semi
group but not a monoid 
< A, *> is a
monoid but not a group 
< A, *> is a
group but not an abelian group 
30 
The conjunctivenormal form of thefollowing is pA(p^q)  qAp  pAq  p^q  q^p 