Homework Answers
Answers: C E
Explanation
Given is in the for a <-> b
a = c -> d
b = e ^ f
C: Uses Contraposition of a which is ~d -> ~c
E: Uses Simplification that a -> b and b -> a must be
true.
Used b -> a
--------------------------------------
Hit the thumbs up if you are fine with the answer. Happy
Learning!
Add Answer to:
In order to prove this proposition: (P (x)-+ Q (z)) <-(R (z) Л Q (z))you must prove which of the following propositi...
Please answer question 1 and 2. (1) Let p, q be propositions. Construct the truth table for the following proposition: (2) Let X be the set of all students in QC and let Y be the set of all classes in...
Please answer question 1 and
2.
(1) Let p, q be propositions. Construct the truth table for the following proposition: (2) Let X be the set of all students in QC and let Y be the set of all classes in the Math Department available for QC students in the Fall 2019. Leyt P(z, y) be the proposition of the course y. Write down the following propositions using quantifiers: e Some QC students read the description of each course in...
10. Let p(x) +1. Let E be the splitting field for p(x) over Q. a. Find the resolvent cubic R(z). ...
Part D,E,F,G
10. Let p(x) +1. Let E be the splitting field for p(x) over Q. a. Find the resolvent cubic R(z). b. Prove that R(x) is irreducible over Q. c. Prove that (E:Q) 12 or 24. d. Prove: Gal(E/Q) A4 or S4 e. If p(x) (2+ az+ b)(a2 + cr + d), verify the calculations on page 100 which show that a2 is a root of the cubic polynomial r(x)3-4. 1. f. Prove: r(x) -4z 1 is irreducible in...
Incorrect Question 7 0/5 pts Which of the following proposition is true? (A) The clause {P(a,x,f(g(y))),...
Incorrect Question 7 0/5 pts Which of the following proposition is true? (A) The clause {P(a,x,f(g(y))), P(z,f(z),f(u))} is unifiable and the set MGU = {[z/a], [x/f(a)], [u/g(y)]} is the most general unifier for it. (B) The clause (P(f(a),g(x)), P(7.7)} is not unifiable. (C) The clause {P(a,x), P(z,f(z))} is unifiable and the set MGU {[z/a], [x/f(a)]) is the most general unifier for it. (D) All of the above. (A (B) (C) (D)
Let P, Q ∈ Z[x]. Prove that P and Q are relatively prime in Q[x] if...
Let P, Q ∈ Z[x]. Prove that P and Q are relatively prime in
Q[x] if and only if the ideal (P, Q) of Z[x] generated by P and Q
contains a non-zero integer (i.e. Z ∩ (P, Q) ̸= {0}). Here (P, Q)
is the smallest ideal of Z[x] containing P and Q, (P, Q) := {αP +
βQ|α, β ∈ Z[x]}.
(iii) For which primes p and which integers n ≥ 1 is the
polynomial xn − p...
a. Define what it means for two logical statements to be equivalent b. If P and Q are two statements, show that the statement ( P) л (PvQ) is equivalent to the statement Q^ P c. Write the converse a...
a. Define what it means for two logical statements to be equivalent b. If P and Q are two statements, show that the statement ( P) л (PvQ) is equivalent to the statement Q^ P c. Write the converse and the contrapositive of the statement "If you earn an A in Math 52, then you understand modular arithmetic and you understand equivalence relations." Which of these d. Write the negation of the following statement in a way that changes the...
1 15 oints) Deterine if the following propositions are TRUE or FALSE. Note that p, q...
1 15 oints) Deterine if the following propositions are TRUE or FALSE. Note that p, q r are propositi Px) and P(x.y) are predicates. RUE or FALSE.Note that p, q, r are propositions. (a).TNE 1f2小5or I + 1-3, then 10+2-3or 2 + 2-4. (b).TRvE+1 0 if and only if 2+ 2 5. (d). _ p v T Ξ T, where p is a proposition and T is tautology. V x Px) is equivalent to Vx - Px) (g). ㅡㅡㅡ, y...
How do you show the following propositions are logically equivalent? (a) [(p → q) → r]...
How do you show the following propositions are logically equivalent? (a) [(p → q) → r] ⊕ (p ∧ q ∧ r) and (p ∨ r) ⊕ (p ∧ q) (b) ¬∃x {P(x) → ∃y [Q(x, y) ⊕ R(x, y)] } and (∀x P(x)) ∧ [∀x ∀y(Q(x, y) ↔ R(x, y))] (c) Does [(p → q) ∧ (q → r)] → r implies (p → r) → r?
(P(x),Q(y), R(z)), where P depends only 2. Let S be any surface with boundary curve C, and let F(x,y, z) on r, where Q...
(P(x),Q(y), R(z)), where P depends only 2. Let S be any surface with boundary curve C, and let F(x,y, z) on r, where Q depends only on y, and where R depends only on z. Show that F.dr 0 C
(P(x),Q(y), R(z)), where P depends only 2. Let S be any surface with boundary curve C, and let F(x,y, z) on r, where Q depends only on y, and where R depends only on z. Show that F.dr 0 C
Incorrect Question 10 0/5 pts Which of the following proposition is false? (A) To prove that...
Incorrect Question 10 0/5 pts Which of the following proposition is false? (A) To prove that a formula F in First-Order Logic (FOL) is a valid formula, is sufficient to prove that the formula -F is a contradiction. (B) To prove that a logical consequence F=G where F and G are formulas in FOL is valid, is sufficient to prove that the formula FA-G is a contradiction. (C) The SAT-problem in First Order Logic is a NP-complete problem. (D) Let...
Problem 22: Which of the following sets are countable? 1. N × Z 2. Q x Q x Q 3. R x R 4.(pe N p prime 7. Set of all infinite sequences of zeroes and ones. Problem 22: Which of the following...
Problem 22: Which of the following sets are countable? 1. N × Z 2. Q x Q x Q 3. R x R 4.(pe N p prime 7. Set of all infinite sequences of zeroes and ones.
Problem 22: Which of the following sets are countable? 1. N × Z 2. Q x Q x Q 3. R x R 4.(pe N p prime 7. Set of all infinite sequences of zeroes and ones.
Please answer question 1 and
2.
(1) Let p, q be propositions. Construct the truth table for the following proposition: (2) Let X be the set of all students in QC and let Y be the set of all classes in the Math Department available for QC students in the Fall 2019. Leyt P(z, y) be the proposition of the course y. Write down the following propositions using quantifiers: e Some QC students read the description of each course in...
Part D,E,F,G
10. Let p(x) +1. Let E be the splitting field for p(x) over Q. a. Find the resolvent cubic R(z). b. Prove that R(x) is irreducible over Q. c. Prove that (E:Q) 12 or 24. d. Prove: Gal(E/Q) A4 or S4 e. If p(x) (2+ az+ b)(a2 + cr + d), verify the calculations on page 100 which show that a2 is a root of the cubic polynomial r(x)3-4. 1. f. Prove: r(x) -4z 1 is irreducible in...
Incorrect Question 7 0/5 pts Which of the following proposition is true? (A) The clause {P(a,x,f(g(y))), P(z,f(z),f(u))} is unifiable and the set MGU = {[z/a], [x/f(a)], [u/g(y)]} is the most general unifier for it. (B) The clause (P(f(a),g(x)), P(7.7)} is not unifiable. (C) The clause {P(a,x), P(z,f(z))} is unifiable and the set MGU {[z/a], [x/f(a)]) is the most general unifier for it. (D) All of the above. (A (B) (C) (D)
Let P, Q ∈ Z[x]. Prove that P and Q are relatively prime in
Q[x] if and only if the ideal (P, Q) of Z[x] generated by P and Q
contains a non-zero integer (i.e. Z ∩ (P, Q) ̸= {0}). Here (P, Q)
is the smallest ideal of Z[x] containing P and Q, (P, Q) := {αP +
βQ|α, β ∈ Z[x]}.
(iii) For which primes p and which integers n ≥ 1 is the
polynomial xn − p...
a. Define what it means for two logical statements to be equivalent b. If P and Q are two statements, show that the statement ( P) л (PvQ) is equivalent to the statement Q^ P c. Write the converse and the contrapositive of the statement "If you earn an A in Math 52, then you understand modular arithmetic and you understand equivalence relations." Which of these d. Write the negation of the following statement in a way that changes the...
1 15 oints) Deterine if the following propositions are TRUE or FALSE. Note that p, q r are propositi Px) and P(x.y) are predicates. RUE or FALSE.Note that p, q, r are propositions. (a).TNE 1f2小5or I + 1-3, then 10+2-3or 2 + 2-4. (b).TRvE+1 0 if and only if 2+ 2 5. (d). _ p v T Ξ T, where p is a proposition and T is tautology. V x Px) is equivalent to Vx - Px) (g). ㅡㅡㅡ, y...
(P(x),Q(y), R(z)), where P depends only 2. Let S be any surface with boundary curve C, and let F(x,y, z) on r, where Q depends only on y, and where R depends only on z. Show that F.dr 0 C
(P(x),Q(y), R(z)), where P depends only 2. Let S be any surface with boundary curve C, and let F(x,y, z) on r, where Q depends only on y, and where R depends only on z. Show that F.dr 0 C
Incorrect Question 10 0/5 pts Which of the following proposition is false? (A) To prove that a formula F in First-Order Logic (FOL) is a valid formula, is sufficient to prove that the formula -F is a contradiction. (B) To prove that a logical consequence F=G where F and G are formulas in FOL is valid, is sufficient to prove that the formula FA-G is a contradiction. (C) The SAT-problem in First Order Logic is a NP-complete problem. (D) Let...
Problem 22: Which of the following sets are countable? 1. N × Z 2. Q x Q x Q 3. R x R 4.(pe N p prime 7. Set of all infinite sequences of zeroes and ones.
Problem 22: Which of the following sets are countable? 1. N × Z 2. Q x Q x Q 3. R x R 4.(pe N p prime 7. Set of all infinite sequences of zeroes and ones.
Most questions answered within 3 hours.
-
Brown Corporation makes four products in a single facility.
These products have the following unit product...
asked 1 minute from now -
20% of all customers subscribe to phone service.
70% of all customers subscribe to internet service....
asked 15 minutes ago -
Write a program to solve the Josephus problem, with the following
modification:
Sample Input:
./a.out n...
asked 2 hours ago -
At the start of a CD it is spinning at a rate of 525 rpm
(revolutions...
asked 3 hours ago -
4. Without doing any calculations, predict whether the observed
∆T would increase, decrease or remain the...
asked 4 hours ago -
Based on the range, which of the following sets of scores has
the greatest variability? 3,...
asked 5 hours ago -
Ripples in a pond travel at a velocity of 3 m/s with one peak
passing a...
asked 5 hours ago -
A man stands on the roof of a building of height 13.0 mm and
throws a...
asked 5 hours ago -
The extent to which assets are financed by borrowed funds and
other liabilities is indicated by:...
asked 6 hours ago -
Explain in detail
Germany is the fifth largest economy
explain what goods and services Germany specializes...
asked 7 hours ago -
The density of platinum is 21.45 g/mL. If a cube of platinum
with a mass of...
asked 7 hours ago -
Accounts Receivable
Sales
A/R Posting
Extended Sales Invoice
Packing Slip
Compare invoice to packing slip 2...
asked 7 hours ago