Question

Define a Venn diagram and a predicate-logic expression for each of these claims: a. all students are persons b. some students are CS majors c. not all CS majors like video games

Answer #1

Solution:-

a) Assuming P(x) denotes 'x is person' then the statement All students are persons can be represented as where domain constitutes All students.

b) Assuming S(x) denotes ' x is a student' , C(x) denotes ' x has
taken CS major' then the statement Some students are CS majors can
be represented as
where domain constitutes students in the class.

c) Assuming C(x) denotes ' x has taken CS major ' , V(x) denotes '
x likes video games' then the statement Not all CS majors like
video games can be represented as
where domain constitutes students in the class.

Convert the following givens into formal predicate logic.
Define predicates as necessary. Then, negate the predicate
sentence. Push all negations to the closest terms
a) There are at least two people who everyone knows. Let the
domain be people.
b) Every student takes at least two classes. Let the domain be
people and classes.
c) Someone is left handed and someone is tall, but no one is
both. Let the domain be people
d) All students know each other. Let...

Convert the following givens into formal predicate logic. Define
predicates as necessary. Then, negate the predicate sentence. Push
all negations to the closest terms
a) There are at least two people who everyone knows. Let the
domain be people.
b) Every student takes at least two classes. Let the domain be
people and classes.
c) Someone is left handed and someone is tall, but no one is
both. Let the domain be people
d) All students know each other. Let...

The domain for the first input variable to predicate T is a set
of students at a university. The domain for the second input
variable to predicate T is the set of Math classes offered at that
university. The predicate T(x, y) indicates that student x has
taken class y. Sam is a student at the university and Math 101 is
one of the courses offered at the university.
Give a logical expression for each sentence. Please provide some
explanation...

A group of college DJs surveyed students to find out what music
to plan for their upcoming parties. Thirty percent of the students
preferred dubstep, 25% of the students liked trance music, and 20%
wanted to hear only house music. Fifteen percent of the respondents
selected both dubstep and trance.
(A) Define event A = {a student likes dubstep} and event B = {a
student likes trance music}. What are the values of P(A) and
P(B)?
(B) Describe what P(A...

DISCRETE MATHS [ BOOLEANS AND LOGIC] Please answer
all
Exercise 1.7.1: Determining whether a quantified statement about
the integers is true.
infoAbout
Predicates P and Q are defined below. The domain of discourse is
the set of all positive integers.
P(x): x is prime
Q(x): x is a perfect square (i.e., x = y2, for some
integer y)
Indicate whether each logical expression is a proposition. If
the expression is a proposition, then give its truth value.
(c)
∀x Q(x)...

Using the following data, build a Venn diagram and then answer
the following questions by filling in each blank with the
correct number.
In a survey of 120 customers of the Rufus Company regarding
their purchases of sweatshirts, the following data were
obtained.
45 buy those sweatshirts sold under the Rufus label.
60 buy those sweatshirts sold under the Wolf label.
56 buy those sweatshirts sold under the Finite label.
23 buy those sweatshirts sold under the Rufus and Wolf...

Suppose the Dean of our college claims that, the average GPA
for all students in the college is at least 3.00, with standard
deviation 0.4. However, from a class with 25 students,
we find the class average GPA is 2.80. Can we reject the
dean’s claim at significance level 0.05? (We conduct a hypothesis
testing).
a). H0:
mu=3.00, Ha:
b). Calculate test statistic, here is
z-value.
c). Find pvalue.
d). Make your decision.

If you wanted to estimate the mean height of all the students at
UW Madison, which one of the following sampling strategies would be
best? Why? (Note that none of the methods are true simple random
samples.) (a) Measure the heights of 100 students found in the gym
during basketball intramurals. (b) Measure the heights of the
engineering majors. (c) Measure the heights of the students
selected by choosing the first name on each page of a list of
students...

In a room there are three students, each of which is equally
likely to be male or female
independently of the others. Define the events:
A = {all the students are of the same sex},
B = {there is at most one female},
C = {the group of three students includes a male and a female}.
(a) Find sets A, B, and C then determine the event
probabilities
(b) Find P(A \ B), P(B − A), and P(A|B).
Are A...

Suppose it is known that 40% of all college students work full
time. Define a success as "a student works full time". (a) If we
randomly select 12 college students, what is the probability that
exactly 3 of the 12 students work full time? (show 5 decimal
places) (b) If we randomly select 12 college students, what is the
probability that at least 3 of the 12 work full time? (show 5
decimal places) (c) In questions (a) and (b)...

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