Question:

I am doing homework, but confused with some questions I will provide my solutions to some of them, please check for mistakes and explain why. 

1. In this question, the domain of discourse is the set of people in our IST 230 class.  Define the following predicates:

            T(x): x is more than six feet tall.

            S(x): x is less than five feet tall.

            Translate the following English statements into a logical expression with the same meaning.

a) "No one in our IST 230 class is both more than six feet tall and less than five feet tall."

b) "Everyone in our IST 230 class is both greater than or equal to five feet tall and less than or equal to six feet tall."

I have solutions but didn't know how to add math formulas here

2. . Prove the following statement using the format used in the answer provided in the practice problems for Lesson 1:  If x is an odd integer, then x + 2 is an odd integer.

no solution

3. Let sets A and B be defined as follows:

            A = {Tom, Bo}

            B = {Java, Python, R}

a. List as a set of ordered pairs one 1-1 function from A to B, or explain why no such function exists. {(Tom,Java), (Bo, R)

b. List as a set of ordered pairs one onto function from A to B, or explain why no such function exists.  {(Tom,Java), (Tom, Python), (Tom,R)}

 

6. Write an algorithm in pseudo-code with the following input and output.

Input: a₁, a₂,..., a_n, a sequence of integers, where n is greater than 5.

Output: The average of the last 5 integers in the sequence. Use auxiliary variables as needed.

            Sum: = 0

For(i = n; i >n-5;i--){

Sum = sum + a_i;}

Average = sum/5)

Return average;

13.  A husband, wife, and their two children line up for a photo. How many ways can this be done if the two children must be next to each other? (Be sure to show your work.)  (10 points)

There are 3 ways how children may be seated: 1)both at left 2)both at right 3)both at the center with permutation of parents, then

3*2! = 6 possible combinations.

14. Must it be true that in a group of ten people, each person's birthday falls in a different month (disregarding year)? Explain. 

It doesn't must to be true, because in a sample of 10 people, they all may have birthday in the same month or even at the same day. Since there are 10 people and 12 months, then there is a possibility of them having birthday at different months, but it doesn't mean it will always be the case.

Chapter 11

15. Consider the experiment of flipping a fair coin ten times. What is the probability of obtaining exactly one heads? 

final probability i got : 5/512