Solving Q.7 with Truth Tables: What Is the Right Conclusion?

  • MHB
  • Thread starter ertagon2
  • Start date
In summary, the conversation discusses the solution to two questions involving truth tables and determining the truth value of statements. The speaker's answer to question 6 is confirmed to be correct, and for question 7, they have two possible solutions where one of the two given conditions is true. The conclusion is that the answer to the first question is "true" and the answer to the second question is also "true" based on the given solutions.
  • #1
ertagon2
36
0
Hi so this is my homework
View attachment 7701
View attachment 7701
I had no problems solving q.6 using truth tables. (Please check if right)
But when solving q.7 i was faced with a question.
I got 2 matches in my truth table.
ABCA...B...C...
TFTTFT
TTFTTF

I was told by my professor that for answer to be right the right side must give the same result as left.
But now I have two matches (left side=right side) what conclusion do i draw from this ?
 

Attachments

  • mathshomework1.png
    mathshomework1.png
    11.8 KB · Views: 105
Physics news on Phys.org
  • #2
ertagon2 said:
Hi so this is my homeworkI had no problems solving q.6 using truth tables. (Please check if right)
But when solving q.7 i was faced with a question.
I got 2 matches in my truth table.
ABCA...B...C...
TFTTFT
TTFTTF

I was told by my professor that for answer to be right the right side must give the same result as left.
But now I have two matches (left side=right side) what conclusion do i draw from this ?
Hi ertagon2,

Your answer to Q6 is correct.

For Q7, I understand that you copied the two rows corresponding to the two matches; if this is the case, they are correct.

What this means is that there are two solutions to the question of who is a knight and who is a knave.

However, that is not the question you are asked. The first question is about the statement "exactly one of B and C is a knave but you can't tell which".

Note that, in each of the two solutions, it is true that exactly one of B and C is a knave: the first part of the statement is true. Furthermore, as there are two possible solutions (B or C is the knave), it is also true that you can't tell which, and that is the second part of the statement. The answer to the question is therefore "true".

For the second question, note that, in each of the two solutions, A is a knight. The answer is therefore also "true" in this case.
 
  • #3
castor28 said:
Hi ertagon2,

Your answer to Q6 is correct.

For Q7, I understand that you copied the two rows corresponding to the two matches; if this is the case, they are correct.

What this means is that there are two solutions to the question of who is a knight and who is a knave.

However, that is not the question you are asked. The first question is about the statement "exactly one of B and C is a knave but you can't tell which".

Note that, in each of the two solutions, it is true that exactly one of B and C is a knave: the first part of the statement is true. Furthermore, as there are two possible solutions (B or C is the knave), it is also true that you can't tell which, and that is the second part of the statement. The answer to the question is therefore "true".

For the second question, note that, in each of the two solutions, A is a knight. The answer is therefore also "true" in this case.

Thanks. I just wanted to make sure that my undertstanding is right.
 

FAQ: Solving Q.7 with Truth Tables: What Is the Right Conclusion?

1. What is a truth table?

A truth table is a logical diagram that shows all possible combinations of inputs and their corresponding outputs for a logical statement or argument. It is used to determine the validity or consistency of an argument.

2. How do you use a truth table to solve a problem?

To use a truth table to solve a problem, you first need to list out all the possible combinations of inputs for the given statement. Then, using logical operators like AND, OR, and NOT, you can determine the output for each combination. The final column in the truth table represents the conclusion or the right answer.

3. What is the purpose of solving Q.7 with truth tables?

Solving Q.7 with truth tables allows us to determine the correct conclusion for a given logical statement or argument. It helps to identify any flaws or inconsistencies in the argument and ensures that the conclusion is valid and based on the given inputs.

4. Can a truth table be used to solve any type of problem?

Truth tables are primarily used to solve problems related to propositional logic, which deals with the relationships between propositions or statements. They can also be used in other branches of mathematics and logic, such as Boolean algebra and computer science.

5. Are there any limitations to using truth tables?

While truth tables are a useful tool for solving logical problems, they can become complex and time-consuming for larger statements with multiple inputs. In such cases, other methods like logical equivalences and proof techniques may be more efficient. Additionally, truth tables can only be used for statements with a finite number of inputs.

Similar threads

Replies
5
Views
2K
Replies
2
Views
1K
Replies
1
Views
1K
Replies
5
Views
2K
Replies
1
Views
982
Replies
1
Views
3K
Replies
2
Views
1K
Back
Top