Now this is confusing

Logic Level 2

I met that same friend of mine once again one day who lies and tells the truth on alternate days.

I asked him, "Will you lie today?"

He said," No, I will not."

On the same day, I asked again, "I think you lied just now, didn't you?"

He said,"No, I did not lie!."

On the basis of the above statement it can be said that:

Can you catch some liars for me. Here are some of them who make statements worth deceiving

Cannot be determined It is an impossible scenario He was telling the truth that day He was lying that day

1 solution

Shawn Franchi
Apr 27, 2016

If we call the friend $A$ , the meaningful content of $A$ 's claims can be summarized in two statements.

$1.$ $A$ will not lie today.

$2.$ Statement $1$ is not false.

We will evaluate this by cases.

Case 1. $A$ is telling the truth today. Assume $A$ is truthful today. Then $1$ and $2$ should both be true. We note that since $A$ is telling the truth today, $1$ is true. Statements $1$ and $2$ are logically equivalent, in that there is a biconditional relationship such that $1$ if and only if $2$ . Hence both statements are true, and no contradiction arises.

Case 2. $A$ is lying today. Assume $A$ is lying today. Then $1$ and $2$ should both be false. We note that since $A$ is lying today, $1$ is false. Statements $1$ and $2$ are logically equivalent, in that there is a biconditional relationship such that $1$ if and only if $2$ . Hence both statements are false, and no contradiction arises.

Neither assumption leads to a contradiction, thus $A$ is either truthful today or else $A$ is lying today, but there is no way to tell which.

Now this is confusing

Can you catch some liars for me. Here are some of them who make statements worth deceiving

1 solution

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