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 many admire Curly, but not Larry nor Moe? | 17 | 16 | 18 | 15 | |

3 | How many admire Larry or Curly? | 77 | 78 | 30 | 31 | |

4 | How many admire exactly one of the Stooges? | 28 | 27 | 29 | 26 | |

5 | How many admire exactly two of the Stooges? | 31 | 30 | 29 | 32 | |

6 | How many admire Larry ? | 49 | 45 | 47 | 42 | |

7 | How many admire all the three of the stooges? | 26 | 24 | 30 | 40 | |

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

9 | How many admire Moe ? | 48 | 49 | 50 | 51 | |

10 | How many admire 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 12 students 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 to answer 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 n B represents: | all elements in either A and B | all elements in both A and B | all elements that are in A but not B | all sets that include A and B |

11 | A non empty set S which is closed with a binary operation ‘*’ is called group if | The binary operation is associative | There exists identity element with respect to the binary operation. | There exist a unique inverse of each element of S with respect to the binary operation | All A, B & C hold. |

12 | There are thirty-four possible (not isomorphic) graphs with five vertices. Which of the following graphs is isomorphic to its OWN compliment? | The complete graph on 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 thefollowing sets are
semigroups? |
The natural numberswith respect to
binary operation addition. |
he set of wordsover a finite
alphabet with the operation v * w = vw of putting the words together. |
he set of allsubsets of a finite
set with the operation 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 theStatement “It is false that he is short or handsome” is | ~(~pVq) | (~pVq) | ~(~P^{A}q) |
(~ P ^{A} q ) |

17 | Write the statementin 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 |
ttttftftt | fttfff | tffttt | fftftf |

19 | You are given abinomial random variable with n = 25 and p = 0.35.
The mean for the random variable is |
8.25 | 8.75 | 8 | 7.85 |

20 | Let p represent thestatement, “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 not play basketball. |
~pAq | ~pA~q | ~(pAq) | ~(pA~q) |

21 | TheContrapositive of the following 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 I take 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 the following is TRUE | The set of all rational negative numbers forms a group under multiplication | The set of all non singular matrices forms a group under multilication | The set of all matrices froms a group under multiplication | Both b & c are true |

25 | G{e , a, b ,c} is an abelian 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 rational numbers is an abelian group under addition | The set of all rational integers is an abelian group under addition | The set of all rational numbers form an abelian group under multiplication | None of these |

28 | If a and b are positive 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 nonsingular 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 semigroup but not a
monoid |
< A, *> is amonoid but not
a group |
< A, *> is agroup but not an
abelian group |

30 | The conjunctive normal form of the following is pA(p^q) | qAp | pAq | p^q | q^p |