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The prosecutor asks, ‘Did you father the child of the murdered victim Miss A?’. Mr. N replies, ‘The claim that I had an affair with Miss A and that I didn’t father her child is false’. In response to the prosecutor’s request for a clarification of this statement, Mr. N says, ‘What I mean is that there is at least one falsehood in the claim that I had an affair with Miss A and that I didn’t father her child.’ The prosecutor then asks, ‘Did you have an affair with Miss A?’ Mr. N replies, ‘Yes, I did.’ Assuming that Mr. N uses language in the usual way, but without knowing whether Mr. N is truthful in answering these questions, what can you deductively infer from Mr. N’s answers? (Note: When my statement X implies statement Y, whether I intend to state Y is irrelevant. X implies Y just when Y follows logically from X. For example, when I say that I’m a man, my claim implies another claim that I’m a human being, whether or not I intend to make the latter claim.)

I. Mr. N had an affair with Miss Α.

II. Mr. N did not father Miss A’s child.

III. Mr. N implied the claim that he had fathered Miss A’s child.

IV. Mr. N implied the claim that he had not fathered Miss A’s child.

A. I, II

B. Only III

C. Only IV

D. II, III

So this question has a few premises, and asked us to deductively infer the "conclusion" if i am not wrong. So the premise says that

  1. Mr N say that there is at least one false statement in the claim that he had an affair with Miss A and that he didn’t father her child.

  2. Mr N claimed he did had an affair with Miss A.

Hence to me it logically follows that Mr N fathered the child since Mr N says that at least one of the statement he said is false. So if having an affair with Mr N is not false, then he did not father her child must be false.

So is the answer just simply B)? I am not sure why the question mentioned without knowing whether Mr. N is truthful in answering these questions. Does that have an impact in our deductively inferring of Mr N's answers?

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    Let A be having an affair and F be fathering a child. The first premise is ¬(A∧¬F)=¬A∨F, the second one is A. If both are true then F is true, so I guess he "implied" F. Since he might have lied we can not say anything as to what in fact happened (I or II), hence B. – Conifold Oct 13 '18 at 20:12

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