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Recent questions tagged mathematicallogic
Webpage for Mathematical Logic
Important Question Types:
Checking validity of First Order Logic Statements
Checking validity of Propositional Logic
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Kenneth Rosen Edition 7th Exercise 1.7 Question (Page No. 91)
Use a direct proof to show that every odd integer is the difference of two squares.
asked
19 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

6
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kennethrosen
discretemathematics
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2
Kenneth Rosen Edition 7th Exercise 1.7 Question 6 (Page No. 91)
Use a direct proof to show that the product of two odd numbers is odd.
asked
19 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

4
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kennethrosen
discretemathematics
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propositionallogic
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1
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Kenneth Rosen Edition 7th Exercise 1.7 Question 5 (Page No. 91)
Prove that if $m+n$ and $n+p$ are even integers, where $m, n$,and $p$ are integers, then $m+p$ is even. What kind of proof did you use?
asked
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Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

3
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kennethrosen
discretemathematics
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4
Kenneth Rosen Edition 7th Exercise 1.7 Question 4 (Page No. 91)
Show that the additive inverse, or negative, of an even number is an even number using a direct proof.
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in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

2
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kennethrosen
discretemathematics
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0
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5
Kenneth Rosen Edition 7th Exercise 1.7 Question 3 (Page No. 91)
Show that the square of an even number is an even number using a direct proof
asked
19 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

3
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kennethrosen
discretemathematics
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0
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0
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6
Kenneth Rosen Edition 7th Exercise 1.7 Question 2 (Page No. 91)
Use a direct proof to show that the sum of two even integers is even.
asked
19 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

2
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kennethrosen
discretemathematics
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0
votes
1
answer
7
Kenneth Rosen Edition 7th Exercise 1.7 Question 1 (Page No. 91)
Use a direct proof to show that the sum of two odd integers is even.
asked
19 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

4
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kennethrosen
discretemathematics
mathematicallogic
0
votes
0
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8
Kenneth Rosen Edition 7th Exercise 1.6 Question 35 (Page No. 80)
Determine whether this argument, taken from Kalish and Montague [KaMo64], is valid. If Superman were able and willing to prevent evil,he would do so. If Superman were unable to prevent evil, he would be impotent; ... does not prevent evil. If Superman exists, he is neither impotent nor malevolent. Therefore, Superman does not exist.
asked
20 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

4
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kennethrosen
discretemathematics
propositionallogic
mathematicallogic
difficult
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9
Kenneth Rosen Edition 7th Exercise 1.6 Question 34 (Page No. 80)
The Logic Problem, taken from WFF'N PROOF, The Game of Logic, has these two assumptions:1. Logic is difficult or not many students like logic. 2. If mathematics is easy, then logic is not difficult. By translating ... not easy. That if not many students like logic, then either mathematics is not easy or logic is not difficult.
asked
20 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

2
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kennethrosen
discretemathematics
mathematicallogic
propositionallogic
difficult
0
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1
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10
Kenneth Rosen Edition 7th Exercise 1.6 Question 33 (Page No. 80)
Use resolution to show that the compound proposition $(p \vee q) \wedge (\sim p \vee q) \wedge (p \vee \sim q) \wedge (\sim p \vee \sim q)$ is not satisfiable.
asked
20 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

8
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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11
Kenneth Rosen Edition 7th Exercise 1.6 Question 32 (Page No. 80)
Show that the equivalence $p \wedge \sim p \equiv F$ can be derived using resolution together with the fact that a conditional statement with a false hypothesis is true. [Hint:Let $q=r=F$ in resolution.]
asked
20 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

3
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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votes
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12
Kenneth Rosen Edition 7th Exercise 1.6 Question 31 (Page No. 80)
Use resolution to show that the hypotheses “It is not raining or Yvette has her umbrella,” “Yvette does not have her umbrella or she does not get wet,” and “It is raining or Yvette does not get wet” imply that “Yvette does not get wet.”
asked
20 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

3
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
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Kenneth Rosen Edition 7th Exercise 1.6 Question 30 (Page No. 80)
Use resolution to show the hypotheses “Allen is a bad boy or Hillary is a good girl” and “Allen is a good boy or David is happy” imply the conclusion “Hillary is a good girl or David is happy.”
asked
20 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

2
views
kennethrosen
discretemathematics
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0
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14
Kenneth Rosen Edition 7th Exercise 1.6 Question 29 (Page No. 80)
Use rules of inference to show that if $\forall x (P(x) \vee Q(x))$, $\forall x (\sim Q(x) \vee S(x)), \forall x (R(x) \rightarrow \sim S(x)),$ and $\exists x \sim P(x)$ are true, then $\exists x \sim R(x)$ is true.
asked
20 hours
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

4
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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15
Kenneth Rosen Edition 7th Exercise 1.6 Question 28 (Page No. 80)
Use rules of inference to show that if $\forall x (P(x) \vee Q(x))$ and $\forall x ((\sim P(x) \wedge Q(x)) \rightarrow R(x))$ are true, then $\forall x (\sim R(x) \rightarrow P(x))$ is also true, where the domains of all quantifiers are the same.
asked
1 day
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

6
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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answers
16
Kenneth Rosen Edition 7th Exercise 1.6 Question 27 (Page No. 80)
Use rules of inference to show that if $\forall x (P(x) \rightarrow (Q(x) \wedge S(x)))$ and $\forall x ( P(x) \wedge R(x))$ are true, then $\forall x (R(x) \wedge S(x))$ is true.
asked
1 day
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

4
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
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17
Kenneth Rosen Edition 7th Exercise 1.6 Question 26 (Page No. 80)
Justify the rule of universal transitivity, which states that if $\forall x (P(x) \rightarrow Q(x))$ and $\forall x(Q(x) \rightarrow R(x))$ are true, then $\forall x (P(x) \rightarrow R(x))$ is true, where the domains of all quantifiers are the same.
asked
1 day
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

4
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
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18
Kenneth Rosen Edition 7th Exercise 1.6 Question 25 (Page No. 80)
Justify the rule of universal modus tollens by showing that the premises $ \forall x (P(x) \rightarrow Q(x)) $ and $\sim Q(a)$for $a$ particular element $a$ in the domain, imply $\sim P(a)$
asked
1 day
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
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3
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kennethrosen
discretemathematics
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19
Kenneth Rosen Edition 7th Exercise 1.6 Question 18 (Page No. 79)
What is wrong with this argument? Let $S(x, y)$ be “$x$ is shorter than $y$.” Given the premise $\exists s S(s, Max)$, it follows that $S(Max, Max)$. Then by existential generalization it follows that $\exists x S(x,x)$, so that someone is shorter than himself.
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1 day
ago
in
Mathematical Logic
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Pooja Khatri
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8.9k
points)

3
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kennethrosen
discretemathematics
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20
Kenneth Rosen Edition 7th Exercise 1.6 Question 17 (Page No. 79)
What is wrong with this argument? Let $H(x)$ be “$x$ is happy.” Given the premise $\exists x H(x)$, we conclude that $H(Lola)$. Therefore, Lola is happy.
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1 day
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

4
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discretemathematics
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0
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21
Kenneth Rosen Edition 7th Exercise 1.6 Question 16 (Page No. 79)
For each of these arguments determine whether the argument is correct or incorrect and explain why. Everyone enrolled in the university has lived in a dormitory. Mia has never lived in a dormitory. Therefore,Mia is not enrolled ... set at least a dozen traps. Hamilton is a lobsterman. Therefore, Hamilton sets at least a dozen traps
asked
1 day
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

3
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kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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22
Kenneth Rosen Edition 7th Exercise 1.6 Question 15 (Page No. 79)
For each of these arguments determine whether the argument is correct or incorrect and explain why. All students in this class understand logic. Xavier is a student in this class. Therefore, Xavier understands logic. Every ... granola every day is healthy. Linda is not healthy. Therefore, Linda does not eat granola every day.
asked
1 day
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

2
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kennethrosen
discretemathematics
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23
Kenneth Rosen Edition 7th Exercise 1.6 Question 14 (Page No. 79)
For each of these arguments, explain which rules of inference are used for each step. Linda, a student in this class, owns a red convertible.Everyone who owns a red convertible has gotten at least one speeding ticket. ... France. Everyone who goes to France visits the Louvre. Therefore, someone in this class has visited the Louvre.
asked
1 day
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

2
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kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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Kenneth Rosen Edition 7th Exercise 1.6 Question 13 (Page No. 79)
For each of these arguments, explain which rules of inference are used for each step. Doug, a student in this class, knows how to write programs in JAVA. Everyone who knows how to write programs in JAVA can get a high ... has never seen the ocean. Therefore, someone who lives within 50 miles of the ocean has never seen the ocean.
asked
1 day
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

3
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kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
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25
Kenneth Rosen Edition 7th Exercise 1.6 Question 9 (Page No. 78)
For each of these collections of premises, what relevant conclusion or conclusions can be drawn? Explain the rules of inference used to obtain each conclusion from the premises. If I take the day off, it either rains or snows. I took ... gnaw their food. Mice are rodents. Rabbits do not gnaw their food. Bats are not rodents.
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in
Mathematical Logic
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Pooja Khatri
Loyal
(
8.9k
points)

2
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kennethrosen
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26
Kenneth Rosen Edition 7th Exercise 1.6 Question 8 (Page No. 78)
What rules of inference are used in this argument? “No man is an island. Manhattan is an island. Therefore, Manhattan is not a man.”
asked
1 day
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

3
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kennethrosen
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27
Kenneth Rosen Edition 7th Exercise 1.6 Question 7 (Page No. 78)
What rules of inference are used in this famous argument? “All men are mortal. Socrates is a man. Therefore,Socrates is mortal.”
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ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

3
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kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
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28
Kenneth Rosen Edition 7th Exercise 1.6 Question 5 (Page No. 78)
Use rules of inference to show that the hypotheses “Randy works hard,” “If Randy works hard, then he is a dull boy,”and “If Randy is a dull boy, then he will not get the job”imply the conclusion “Randy will not get the job.”
asked
1 day
ago
in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

3
views
kennethrosen
discretemathematics
mathematicallogic
propositionallogic
0
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29
Kenneth Rosen Edition 7th Exercise 1.6 Question 4 (Page No. 78)
What rule of inference is used in each of these arguments? Kangaroos live in Australia and are marsupials. Therefore, kangaroos are marsupials. It is either hotter than 100 degrees today or the pollution is dangerous. It ... the material . Therefore ,If I work all night on this homework, Then I will understand the material.
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1 day
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in
Mathematical Logic
by
Pooja Khatri
Loyal
(
8.9k
points)

2
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kennethrosen
discretemathematics
mathematicallogic
propositionallogic
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Kenneth Rosen Edition 7th Exercise 1.6 Question 3 (Page No. 78)
What rule of inference is used in each of these arguments? Alice is a mathematics major. Therefore, Alice is either a mathematics major or a computer science major. Jerry is a mathematics major and a computer science major. Therefore, ... stay in the sun too long, then I will sunburn. Therefore, if I go swimming, then I will sunburn
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1 day
ago
in
Mathematical Logic
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Pooja Khatri
Loyal
(
8.9k
points)

3
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