Sample Research Paper

1. Please provide a short definition of the following:

a.Set

b. Subset

c.Proper Subset

d. Compliment of a set

e. Union of a set

f. Intersection of a set

a. A set can be defined as a collection of items. These items are called elements of the set. A set can be finite or infinite. A finite set is one that has finite number of elements. An infinite set is a set which does not limit the number of element in the set.

b. A set “A” is said to a subset of set “B” if  all  elements of set “A” can be found in set “B”. Set “B” is then called Superset of set “A”.

c. A Proper Subset “A” has all its elements in another set “B”. But set “B” does not follow this property.

d. A Union set is a join of two set which contains all elements from both sets, without repetition.

e. An Intersection of two sets is one which contain only those elements where are found in both sets (Waner, 2006).

2. Provide an answer to the following problems: 2. Set X = {5, 7, 11, 16, 21, 702}, Set Y = {2, 5, 8, 11,19, 702}

a. What is the union of Sets X and Y?

The Union of Set X and Y will be  XUY = {2,5,7,8,11,16,19,21,702}.

b. What is the intersection of Sets X and Y

The Intersection of  Set X and Y will be X∩Y = (5,11,702}.

c. Create your own set Z that is a subset of Set X.

A possible subset Z can be : Z = {7,11} (Waner, 2006).

3. Let Set 1 be the entire alphabet. Let Set 2 = {g, h, i,j, k, l}

a. What is the complement of Set 2 in Set 1?

The complement of Set 2 in Set 1 is  : Set1/Set2 = {a,b,c,d,e,f,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.

b. Set 3 = {h,i, j, k}.

Is Set 3 a proper subset of Set 2? Explain your reasoning.

For Set 3 to be a proper subset of Set 2, all its elements must also be in Set 2. However, Set 2 must contain additional elements. Here, both of this properties are followed , hence, Set 3 is a proper subset of set 2 (Waner, 2006).

4. Take out a coin for the following problems:

a. Suppose you are going to flip a coin once. What is the set of possible outcomes for this?

The possible outcome set for this will be  O = {Head,Tail}.

b. Suppose you are going to flip a coin twice. What is the set of possible outcomes for this?

The possible outcome set for this will be O = {(Head,Head), Head,Tail),(Tail,Head),(Tail,Tail)}.

c. If flip a coin twice, what are the chances that you will get one head and one tail (i.e. one in three,one in four, etc.)? Use your answer to the question 3b to get your answer.

The chances of getting one head and one tail are two in four (Waner, 2006).

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