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

[ertagon2]

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.
[table="width: 500, class: grid"]
[tr]
[td]A[/td]
[td]B[/td]
[td]C[/td]
[td]A...[/td]
[td]B...[/td]
[td]C...[/td]
[/tr]
[tr]
[td]T[/td]
[td]F[/td]
[td]T[/td]
[td]T[/td]
[td]F[/td]
[td]T[/td]
[/tr]
[tr]
[td]T[/td]
[td]T[/td]
[td]F[/td]
[td]T[/td]
[td]T[/td]
[td]F[/td]
[/tr]
[/table]

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 ?

 

[castor28]

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.
[TABLE="class: grid, width: 500"]
[TR]
[TD]A[/TD]
[TD]B[/TD]
[TD]C[/TD]
[TD]A...[/TD]
[TD]B...[/TD]
[TD]C...[/TD]
[/TR]
[TR]
[TD]T[/TD]
[TD]F[/TD]
[TD]T[/TD]
[TD]T[/TD]
[TD]F[/TD]
[TD]T[/TD]
[/TR]
[TR]
[TD]T[/TD]
[TD]T[/TD]
[TD]F[/TD]
[TD]T[/TD]
[TD]T[/TD]
[TD]F[/TD]
[/TR]
[/TABLE]

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.

 

[ertagon2]

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.