First Set Currency

Placeholder

Business Mathematics 2

$10.00

SKU: AMSEQ-031 Category:

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