Implication of Paul's Statement

Logic Level 2

Paul: I have exactly one girl friend.

Which of the following is true?

Paul has at most one girl friend.
Paul has at least one girl friend.
Paul has at most one girl friend and at least one girl friend.

1,2, and 3 3 only None of them 2 only 1 only

2 solutions

Paul Ryan Longhas
Aug 26, 2015

Let $x$ be the number of girl friend of Paul. So, $x = 1$ .

Note that by Law of Addition, we know that $p \Rightarrow p$ \/ $q$ where $p$ and $q$ are proposition.

So, $x = 1 \Rightarrow x = 1$ or $x > 1$ shortly $x = 1 \Rightarrow x \geq 1$ . Thus, the statement 1 is true.

Also, $x = 1 \Rightarrow x =1$ or $x < 1$ shortly $x=1 \Rightarrow x \leq 1$ . Thus, the statement 2 is true.

We know that the statement 3 states that $x \leq 1$ at the same time $x \geq 1$ . If we solve the intersection of this two inequality, we solved that $x = 1$ . Thus, the statement 3 is true.

Therefore, 1,2, and 3 are all true.

Lucky Paul.

Daniel Liu - 5 years, 9 months ago

Yes, but Paul's girlfriend may not appreciate statement 2. Paul may soon have at most 0 girlfriends. Unless we are just talking about a friend who just happens to be a girl; then she may be chill with statement 2.

Brian Charlesworth - 5 years, 9 months ago

If statement $2$ stays true but statement $1$ turns out to be false as time passes, perhaps Paul would like to share his girlfriends with others, so all three statements can still be true (hint hint).

Trevor B. - 5 years, 9 months ago

@Trevor B. – Haha. Well, yeah, I think that the girls would have something to say about that arrangement. :P

Brian Charlesworth - 5 years, 9 months ago

@Brian Charlesworth – The girls would loooove to be in an arrangement such that one of them is with me. Absolutely love it. One hundred percent, I guarantee it. Yup.

Trevor B. - 5 years, 9 months ago

@Trevor B. – Yup, girls always appreciate modesty. :)

Brian Charlesworth - 5 years, 9 months ago

@Brian Charlesworth – Haha, I'm actually a reasonably modest person who's not interested in girls at the moment. I think it's funny to examine the mathematics of dating and relationships though ;)

Trevor B. - 5 years, 9 months ago

@Trevor B. – I'm sure that you are quite modest, and that, along with your sense of humor, will stand you in good stead whenever your interest in girls resumes. As for the mathematics of dating, apparently The University of Washington offers a course in the subject. (It would be more timely to teach that in high school, though.) :)

Brian Charlesworth - 5 years, 9 months ago

Hadia Qadir
Sep 1, 2015

1,2 and 3 We can say that Paul has < or equal to 1 gf. Or Paul has > or equal to 1 gf

Implication of Paul's Statement

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