# Research Methods and Report Writing-1A

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SKU: AMSEQ-235 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.

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:

24 admire all three of the Stooges

1 admires none of the Three Stooges

 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) ~(~PAq) (~ 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)<=>(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 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

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