Hands up!

[wolfgang]

Three persons( A,B,and C) are not allowed to speak,but to raise a hand  refering to ( Yes or No ), you don`t know which hand means Yes,and which means No.

How can you know  the persons which is which by asking only three( yes or no) questions.

You may ask one ,two or all of them...as you like.

any  question should be asked to a single person.

Edited September 7, 2014 by wolfgang

[DejMar]

We can make a truth table to do this..

a. If Q is true and X is right-handed, he/she should raise right hand ([1 1] => 1)

b. If Q is true and X is left-handed, he/she should raise right hand ([1 0] => 0)

c. If Q is false and X is right-handed, he/she should raise left hand ([0 1] => 0)

d. If Q is false and X is left-handed, he/she should raise left hand ([0 0] => 1)

This is nothing but an xor operation, can also be stated as is Q' = "the truth value of Q the same as the truth value of saying 'you are right-handed'"

 

This is incorrect. The truth-table does coincide with an XOR operation, but the compound statement is not formulated as an XOR, but as AND. The boolean result is different for the operands if Q is false and X is left-handed, he/she should raise left hand ([0 0] => 0).

 

If person in chair 1 responds to Q1 by raising his right hand, he is person A, and he is (right-handed or not). OR he is person (B or C) and he is left-handed.
If person in chair 2 responds to Q1R Q2 by raising his right hand, he is person B, and he is (right-handed or not) OR he is person (A or C), and he is left-handed.
Etc.

koren was partly correct in recognizing that the questions do not necessarily identify who the person is.
karthickgururaj was on the correct track in recognizing that the solution may rely on self-referential questions.

[karthickgururaj]

 

Hey DejMar!

 

 

 

We can make a truth table to do this..

a. If Q is true and X is right-handed, he/she should raise right hand ([1 1] => 1)

b. If Q is true and X is left-handed, he/she should raise right hand ([1 0] => 0)

c. If Q is false and X is right-handed, he/she should raise left hand ([0 1] => 0)

d. If Q is false and X is left-handed, he/she should raise left hand ([0 0] => 1)

This is nothing but an xor operation, can also be stated as is Q' = "the truth value of Q the same as the truth value of saying 'you are right-handed'"

 

This is incorrect. The truth-table does coincide with an XOR operation, but the compound statement is not formulated as an XOR, but as AND. The boolean result is different for the operands if Q is false and X is left-handed, he/she should raise left hand ([0 0] => 0).

 

If person in chair 1 responds to Q1 by raising his right hand, he is person A, and he is (right-handed or not). OR he is person (B or C) and he is left-handed.
If person in chair 2 responds to Q1R Q2 by raising his right hand, he is person B, and he is (right-handed or not) OR he is person (A or C), and he is left-handed.
Etc.

koren was partly correct in recognizing that the questions do not necessarily identify who the person is.
karthickgururaj was on the correct track in recognizing that the solution may rely on self-referential questions.

 

Maybe I didn't explain well.. but it is still an xor operation.

 

a. If Q is true and X is right-handed, he/she should raise right hand ([1 1] => 1)

b. If Q is true and X is left-handed, he/she should raise right hand ([1 0] => 0)

c. If Q is false and X is right-handed, he/she should raise left hand ([0 1] => 0)

d. If Q is false and X is left-handed, he/she should raise left hand ([0 0] => 1)

 

The "and" on top is not a boolean "and". It is just the plain old English conjunction "and" for joining two parts of the sentence.

 

What we are trying to do is the following: If we need to find the answer to a question Q from a person, we'll ask a different question Q' that will cause the person will raise the right hand if Q is true; left hand if otherwise.  First goal: How to formulate Q' from Q ?

 

To do that, let us designate:

1. The truthfulness of the question "Is the person right-handed?" as X. X is (of course) an unknown - maybe either true or false. Goal is not to find X, but we need to accommodate the fact that X is an unknown in our strategy.

2. The truthfulness of Q as t(Q). t(Q) is not known, and that is what we need to find out to reach the first goal.

3. The truthfulness of Q' as t(Q'). t(Q') is not known, and is not even a desired result (we are looking for truthfulness of Q, not Q'). But it is helpful to understand the underlying workings.

 

Strategy - we list down all possible values for t(Q) and X.

a. Let t(Q) = true => we want right hand to be raised. Further, if X = true, the value of t(Q') must be true (in order for right hand to be raised).

b. Let t(Q) = true => we want right hand to be raised. Further, if X = false, the value of t(Q') must be false (in order for right hand to be raised).

c. Let t(Q) = false => we want left hand to be raised. Further, if X = true, the value of t(Q') must be false (in order for left hand to be raised).

d. Let t(Q) = false => we want left hand to be raised. Further, if X = false, the value of t(Q') must be true (in order for left hand to be raised).

 

So, t(Q') = t(Q) xor X

 

 

Hope that helps..

 

 

[DejMar]

karthickgururaj, it did help me find my error. You are correct, it is not an logical conjunction (AND), yet neither is it a logical disjunction (XOR).



 

The question

"Is the truth value of 'you are person A' the same as truth value of 'you are right-handed'?"
written as a declarative statement,
"The truth value of 'you are person A' is the same as truth value of 'you are right-handed'",
is a logical bi-conditional (XNOR), the negation of an XOR.

The truth-table of the XNOR is
T T = F
T F = T
F T = T
F F = F

The statements of your truth-table example uses a conditional statement (if p then q), with the boolean result of the antecedent, p, being the result of the logical AND (p and q).

If (Q is true and X is right-handed), he/she should raise right hand.
Q is true when the truth-value of the addressed person is not the person identified, and the handedness is correct or when the truth-value of the addressed person is the person identified and the handedness is not correct, else it is false. The consequent "he/she should raise right hand", though is a normative statement due to the the use of the auxiliary verb 'should; and is often treated as having a truth-value of true, but is sometimes considered to have no truth-value. Of course there is an implication that the right hand is raised or not raised as determined by the truth value of Q, in which case the truth value of whether the hand is raised is always identical to that of truth value of Q.

Nonetheless, the XNOR can be utilized in a similar manner as the XOR, which can result in finding the order of A, B, and C -- as you have indicated in your solution.

Edited October 31, 2014 by DejMar

[karthickgururaj]

karthickgururaj, it did help me find my error. You are correct, it is not an logical conjunction (AND), yet neither is it a logical disjunction (XOR).

The question

"Is the truth value of 'you are person A' the same as truth value of 'you are right-handed'?"

written as a declarative statement,

"The truth value of 'you are person A' is the same as truth value of 'you are right-handed'",

is a logical bi-conditional (XNOR), the negation of an XOR.

The truth-table of the XNOR is

T T = F

T F = T

F T = T

F F = F

The statements of your truth-table example uses a conditional statement (if p then q), with the boolean result of the antecedent, p, being the result of the logical AND (p and q).

If (Q is true and X is right-handed), he/she should raise right hand.

Q is true when the truth-value of the addressed person is not the person identified, and the handedness is correct or when the truth-value of the addressed person is the person identified and the handedness is not correct, else it is false. The consequent "he/she should raise right hand", though is a normative statement due to the the use of the auxiliary verb 'should; and is often treated as having a truth-value of true, but is sometimes considered to have no truth-value. Of course there is an implication that the right hand is raised or not raised as determined by the truth value of Q, in which case the truth value of whether the hand is raised is always identical to that of truth value of Q.

Nonetheless, the XNOR can be utilized in a similar manner as the XOR, which can result in finding the order of A, B, and C -- as you have indicated in your solution.

 

I'm not sure where exactly we are differing, but I think it is still XOR.

 

 

Repeating from the previous post, the relation we seek can be expressed by:

a. Let t(Q) = true => we want right hand to be raised. Further, if X = true, the value of t(Q') must be true (in order for right hand to be raised).

b. Let t(Q) = true => we want right hand to be raised. Further, if X = false, the value of t(Q') must be false (in order for right hand to be raised).

c. Let t(Q) = false => we want left hand to be raised. Further, if X = true, the value of t(Q') must be false (in order for left hand to be raised).

d. Let t(Q) = false => we want left hand to be raised. Further, if X = false, the value of t(Q') must be true (in order for left hand to be raised).

 

Or, more concisely:

 

t(Q)     X     t(Q')

  1      1      1   (Note: t(Q) = X)

  1      0      0

  0      1      0

  0      0      1   (Note: t(Q) = X)

 

So, t(Q') = t(Q) xor X

 

There is an other way to express the RHS: "Is the truth value of Q the same as truth value of X?". Because, an XOR operation will be true if the value of both the operands is equal.

 

It comes down to the following now:

a. I want to find the truth value of question Q

b. I do not know the truth value of X (i.e, I don't know whether the person will raise right-hand to signify "yes" or the left hand)

c. So I instead ask a question Q', as "Is the 'truth value of Q' equal to the 'truth value of X'?".

d. Alternatively (and equivalently), I could have also asked, Q' as "(truth value of Q') xor (truth value of X)". But that sounds..well, worse.

e. The person will raise right-hand if Q is true, else left-hand.

 

[DejMar]

karthickgururaj,

There are many articles about logic functions in the internet, almost all agree with the definition of the XOR given in the Wikipedia article "Exclusive or": "Exclusive disjunction or exclusive or is a logical operation that outputs true whenever both inputs differ (one is true, the other is false)." The truth table of the XOR is opposite to the truth table you expected.

Edited October 31, 2014 by DejMar

[DejMar]

(continued from post #31)

Yet, serendipitously, the question you posed for Q is not an XOR, but an XNOR, which yielded the desired truth values you expected.There was just a little confusion as a result of calling it an XOR in your solution post.

I do want to say, I applaud you for formulating a good question in the solution.  And thank you for taking time to explain it to me.
 

[karthickgururaj]

(continued from post #31)

Yet, serendipitously, the question you posed for Q is not an XOR, but an XNOR, which yielded the desired truth values you expected.There was just a little confusion as a result of calling it an XOR in your solution post.

I do want to say, I applaud you for formulating a good question in the solution.  And thank you for taking time to explain it to me.

 

Oops, yes!! Sorry.

 

It is XNOR. I don't know what I was thinking.