I have a few logic questions that I am having difficult with and would be greatful for any insight...
#1
I need to know if this is a real or apparent argument.
A: I saw Bob with Mary last night.
B: You saw Frank, Bob's identical twin, with Marsha last night.
I'm thinking that this is a real arguement...
#2. Also, I need to know if these statements are consistent or inconsistent.
(A and B are two different people)
A: I think Ian is at the tea house.
B: You know very well that Ian is not at the tea house.
I'm thinking consistent...
#3. A. If Hal is happy then Sam is sad.
B. Hal is happy and Sam is sad
For these statments, I need to determine:
a. If A is true, is B necessarily true, false, or undetermined?
b. If B is true, is A necessarily true, false, or undetermined...
c. If A is false, is B necessarily false, true, or undetermined?
d. If B is false, is A necessarily flase, true, or undetermined?
Thanks!
#1 That is an apparent argument. The person does not state a reason as to why he is arguing a difference. We have no "proof".
#2. That would be inconsistent. Again, we have no proof that the disagreement is based on fact.
#3. Statement B is based on fact. Statement A would be an opinion.
#1
I'm having trouble understanding why you say it is not a real arguement. Person A is stating that he saw Bob and person B is saying that person A really saw Frank. How is it possible for the two statements to both be true and thus inconsistent?
#2. Can't person A THINK something but KNOW the opposite (as person B is saying he does) making the two statements consistent?
#3. I do not get your answer to question 3. I am needing to know if I assume that statement A is true, what can I know about statement B (that it's necessarily true, false, or undetermined), and etc. for questions b, c, and d.
I'm thinking the answer would be undetermined in each case. (If A is true, B is undetermined, etc.)
I agree with your answer that each would be undertermined for exactly the reason you stated.
#2...I do not believe that a person can think something that he knows is not true.
Regarding #1... how do you know that I did not see Bob with Mary last night? You can well be mistaken unless you were with me?
Let's go through each question and analyze them step by step:
#1:
To determine if this is a real or apparent argument, we need to examine the structure of the statements.
Statement A: "I saw Bob with Mary last night."
Statement B: "You saw Frank, Bob's identical twin, with Marsha last night."
In this case, Statement A presents a direct observation made by the speaker. Whereas Statement B challenges Statement A by proposing an alternative explanation that involves Bob's identical twin, Frank.
Since both statements are offering contradictory information based on personal observations, this can be categorized as an apparent argument. An apparent argument is when two people present conflicting claims based on their own personal observations or experiences.
#2:
To determine if these statements are consistent or inconsistent, we need to examine the content of each statement.
Statement A: "I think Ian is at the tea house."
Statement B: "You know very well that Ian is not at the tea house."
In this case, Statement A expresses the speaker's belief that Ian is present at the tea house. On the other hand, Statement B asserts that the listener is aware that Ian is not at the tea house.
Since these statements directly conflict with each other, they are inconsistent. When two statements provide contradictory information, they cannot both be true at the same time.
#3:
Let's analyze the relationship between statements A and B:
Statement A: "If Hal is happy, then Sam is sad."
Statement B: "Hal is happy and Sam is sad."
a. If A is true, is B necessarily true, false, or undetermined?
If we assume statement A to be true, it states a conditional relationship between Hal's happiness and Sam's sadness. According to statement A, if Hal is happy, then Sam must be sad. Therefore, if A is true, B is necessarily true.
b. If B is true, is A necessarily true, false, or undetermined?
If we assume statement B to be true, it states that Hal is happy and Sam is sad. However, statement B does not imply a cause-and-effect relationship or a conditional statement like statement A does. Therefore, we cannot determine the truth value of statement A based solely on statement B. So, if B is true, the truth value of A remains undetermined.
c. If A is false, is B necessarily false, true, or undetermined?
If we assume statement A to be false, it means that there is no necessary relationship between Hal's happiness and Sam's sadness. Therefore, statement A being false does not necessarily imply anything about the truth value of statement B. Thus, if A is false, the truth value of B remains undetermined.
d. If B is false, is A necessarily false, true, or undetermined?
If we assume statement B to be false, it means that Hal is not happy and/or Sam is not sad. Since statement A establishes a conditional relationship between Hal's happiness and Sam's sadness, if Sam is not sad, it means Hal cannot be happy according to the conditional statement. Therefore, if B is false, A is necessarily false.
I hope this helps clarify your logic questions! If you have any further questions or need additional explanations, feel free to ask.