Question

Given statement p q, the statement q p is called its converse. Let A be the statement: If it is Tuesday, then you come to campus. (1) Write down the converse of A in English. (2) Is the converse of A true? Explain. (3) Write down the contrapositive of A in English

Let the following statement be given: p = “You cannot swim” q = “You are less than 10 years old” r = “You are with your parents” (1) Use connectives to translate the following statement into formal logic: You can swim if you are at least 10 years old or you are with your parents. (2) Write down the contrapositive of the statement from (1) in the symbols of formal logic. (3) Translate the contrapositive from (2) in English.

Answer #1

I hope you like this.

1. Suppose P and Q are the statements: P: Jack passed math. Q:
Jill passed math.(25 points)
(a) Translate “Jack and Jill both passed math” into symbols.
(b) Translate “If Jack passed math, then Jill did not” into
symbols.
(c) Translate “P ∨ Q” into English.
(d) Translate “¬(P ∧ Q) → Q” into English.
(e) Suppose you know that if Jack passed math, then so did Jill.
What can you conclude if you know that: i. Jill passed math?...

Discrete Mathematics
(a) Let P(x) be the predicate “−10 < x < 10” with domain
Z+ (the set of all positive integers). Find the truth set of
P(x).
(b) Rewrite the statement Everybody trusts somebody in formal
language using the quantiﬁers ∀ and ∃, the variables x and y, and a
predicate P(x,y) that you must deﬁne.
(c) Write the negation of the statement in (b) both formally and
informally.

1. Let D: P = 20 – Q/4. Calculate when ɛ when P = $10.
2. Let D: P = 1/Q^2. Calculate ɛ along the demand curve.
3. Suppose e = -2, if P is up by 3% by how much will total
revenue change?

Let P be the plane given by the equation 2x + y − 3z = 2. The
point Q(1, 2, 3) is not on the plane P, the point R is on the plane
P, and the line L1 through Q and R is orthogonal to the plane P.
Let W be another point (1, 1, 3). Find parametric equations of the
line L2 that passes through points W and R.

Let p=3 and q=17 and let an RSA public-key cryptosystem be
given.
1. Why is the number 8 not a valid encryption-key?
2. We encrypt the number M=8 with the help of the encryption-key
e=3.
Why is the encrypted message C=2?
3. Why is the decryption key d for the encryption-key, (e=3),
equal to 11?
https://en.wikipedia.org/wiki/RSA_(cryptosystem)#Encryption

2. Let market demand be given by Q( P) = 200 ? P. Each firm’s
cost function is C(qi ) = 20qi , where i = 1, 2.
(d) Does each firm have an incentive to increase output? What is
the optimal defection for each firm? What does this imply about the
stability of their collusive agreement?
(e) Suppose that the cost function is now C(qi ) = 20qi + 400.
What is the free-entry number of firms?

5. Let market demand be given by the demand curve Q(p) = 200 ? p
. Each
firm’s cost function is TC(qi) = 20qi; i =1, 2.
(a) Using the Cournot model, find each firm’s output, profit and
price.
(b) Graph each firm’s best-response function. Show the Cournot
equilib- rium.
(c) Suppose that the duopolists collude. Find their joint profit
maximizing price, output, and profit. Also find each firm’s output
and profit.
(d) Does each firm have and incentive to...

1.Write the negation of the following statement in English. Do
not simply add the words “not” or “it is not the case that” or
similar before the existing statement. “Every dog likes
some flavor of Brand XYZ dog food.”
2. Prove that the compound statements are logically equivalent
by using the basic logical equivalences (13 rules). At each step,
state which basic logical equivalence you are using. (p → q) ∧ (¬r
→ q) and (p ∨ ¬r) → q

A small country’s demand curve is given by Q=10-(P/2) and its
supply curve is given by Q=P-5. Assume the world is currently in
free trade and that the price under free trade is $7. What is the
size of the import quota that, when introduced, would be equivalent
(i.e. have the same impact on price and quantity) to the
introduction of a $2 specific import tariff?

2. Suppose the demand for coffee is given by Q(p) = 30 -
p, where p is the price per cup. If the price per cup is $10, then
the price elasticity of demand for coffee is:
Please show all work, step by step
a.
-6.
b.
-1.
c.
-1/2.
d.
-0.55.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 5 minutes ago

asked 6 minutes ago

asked 15 minutes ago

asked 17 minutes ago

asked 26 minutes ago

asked 26 minutes ago

asked 31 minutes ago

asked 35 minutes ago

asked 35 minutes ago

asked 41 minutes ago

asked 46 minutes ago

asked 48 minutes ago