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 A-B | {2,4,6} | {4,6,7} | {9,11,13} | {3,4,6} |
| 5 | Which output expression might indicate a product -of-sums circuit construction? |
A • (B • C) = (A • B) + C |
A+(B + C) = (A-B) + (A-C) | A • (B + C) = (A • B) + (A-C) | (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 thirty-four 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) | ~(~PAq) | (~ 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)<=>(PA~Q) I believe I am on the right path with the following: P Q P=>Q ~(P=>Q) ~Q PA~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 |
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