(2) Which of these are propositions? What are the true values of those that re propositions? Do...

Question

(2) Which of these are propositions? What are the true values of those that re propositions?
1. Do not pass go
2. What time is it?
3. There are no black flies in Maine.
4. 4 + X = 5
5. The moon is made of green cheese.
6. 2ⁿ
  = 100.

( 11) Let
p
and
q
be the propositions

p:
It is below freezing
q: It is snowing
Write these propositions using
p
and
q
and logical connectives (including negations).

It is below freezing and snowing

It is below freezing but not snowing

It is not below freezing and it is not snowing

It is either snowing or below freezing (or both).

If it is below freezing, or it is snowing, but it is not snowing it if is below freezing.

Either it is below freezing or it is snowing, but it is not snowing if it is below freezing.

That it is below freezing is necessary and sufficient for it to be snowing.

(31) Construct a truth table for each of these compound propositions.

(3) You can graduate only if you have completed the requirements of your major and you do not owe money to the university and you do not have an overdue library book. Express your answer in terms of
g: “You can graduate,”
m: “You owe money to the university.”
r: “You have completed the requirements of your major.” And
b: “You have an overdue library book.”

(8) Express these system specifications using the propositions
p
“The user enters a valid password,”
q
“Assess is granted,” and
r
“The user has paid the subscription fee” and logical connectives (including negations).
1. “The user has paid the subscription fee, but does not enter a valid password:
2. “Access is granted whenever the user has paid the subscription fee and enters a valid password”
3. “Access is denied if the user has not paid the subscription fee.”
4. “If the user has not entered a valid password but has paid the subscription fee, then access is granted”.

(24) Relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normal by Smullyan (Sm78]) who can either lie or tell the truth. You encounter three people, A, B, and C. You know one of these people is a knight, one is a knave, and one is a spy. Each of the three people knows the type of person each of other two is. For this situation, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. If there is n unique solution, list all possible solutions or state that there are no solutions.

A says “C is the knave,” B says, “A am the knave,” and C says “B is the knight.”

(6) Let N(x) be the statement “x
has visited North Dakota” where the domain consists of the students in your school. Express each of these quantifications in English.

(11) Let P(x) be the statement “x=x².” If the domain consists of the integers, what are these true values?
1. P(0)
2. P(1)
3. P(2)
4. P(-1)

(32) Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left of a quantifier. Next, express the negation in simple English. (Do not simply use the phrase “It is not the case that.”)
1. Some old doges can learn new tricks.
2. No rabbit knows calculus.
3. Every bird can fly.
4. There is no dog that can talk.
5. There is no one in this class who knows French and Russian.

(2) Determine whether
f
is a function from
Z
to
R
if

(12) Determine whether each of these function from {a, b, c, d} to itself is one-to-one.

(13) Which function is from the above question are onto?

(2a) Find
A+B, where

A= 1 0 4

B= -1 3 5
2 2 -3

2 -3 0

(4b) Find the product
AB, where

A= 1 -3 0

2 2

1 -1

= -1 0 3 -1

005_1gr59zk-hn1uiuiv.docx

David · Accepted Answer

1. Proposition are declarative sentence. Hence (c) and (e) are proposition.
2. (a) p ∧ q
(b) p∧ ∼ q
(c) ∼ q∧ ∼ q
(d) p ∨ q
(e) Sentence is wrong... I think typing mistake. Sentence is ”...... but it
is not snowing it if is below....”
(f) (p ∨ q) ∧ (p→∼ q).
(g) p↔ q.
3. (a)
p q p∧ ∼ q
T T F
T F T
F T F
F F F
(b)
p q p∨ ∼ q
T T T
T F T
F T F
F F T
(c)
p q p∧ ∼ q (p∧ ∼ q)→ q
T T F F
T F T F
F T F F
F F F T
(d)
p q p ∧ q p ∨ q p ∧ q → p ∨ q
T T T T T
T F F T F
F T F T F
F F F F T
(e)
p q (p→ q) (∼ q →∼ p) (p→ q)↔ (∼ q →∼ p)
T T T T T
T F F F T
F T F F T
F F T T T
(f)
p q (p→ q)→ (q → p)
T T T
T F F
F T F
F F T
1
4.
g : Y oucangraduate,
m :

(2) Which of these are propositions? What are the true values of those that re propositions? Do not pass go What time is it? There are no black flies in Maine. 4 + X = 5 The moon is made of green...

Answer To: (2) Which of these are propositions? What are the true values of those that re propositions? Do not...

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