1. ## simple logic

consider thr expressions '(a,b) is a point on y=2x-1' and 'b=2a-1'
what is their relation?
which one implicates the other?
the first to the second or vice-versa?
i replied that that the implication and the converse were true, but it was wrong, apparently. can somebody expalin that?

2. Originally Posted by scouser
consider the expressions '(a,b) is a point on y=2x-1' and 'b=2a-1' what is their relation?
which one implicates the other?
the first to the second or vice-versa?
i replied that that the implication and the converse were true, but it was wrong, apparently. can somebody explain that?
The sad fact is that correct answer is known only to the person who wrote this question.
It would help if we had the exact statement of the question, as well as, the level of rigor expected.

That said, here is my take on an answer.
If (a,b) is a point on the line y=2x-1 then b=2a-1. That is a true statement.

If (a,b) is a point in $\displaystyle R^2$ and b=2a-1 then (a,b) is on the line y=2x-1.
That is also a true statement.

But note the additional conditions I have added. That is what I mean by the level of rigor.

3. actually this question was supposed to be simple. i was asked this question in a revision introduction to proof and reasoning. i was supposed to determine which of those little sign thingies connects the two statements, you know arrow to the left, arrow to the right, arrows on both sides. do you understand what i mean?

4. Originally Posted by scouser
actually this question was supposed to be simple. i was asked this question in a revision introduction to proof and reasoning. i was supposed to determine which of those little sign thingies connects the two statements, you know arrow to the left, arrow to the right, arrows on both sides. do you understand what i mean?
Hi scouser.

The relation between the two statements is “if and only if” (assuming that $\displaystyle a,b\in\mathbb R$ – which I’m sure is in mentioned in your book though you didn’t mention it in your first post). Thus:

$\displaystyle \forall\,a,b\in\mathbb R,\ (a,b)$ is on $\displaystyle y=2x-1\ \color{red}\iff\color{black}\ b=2a-1$

5. Sorry to intervene, but it is instructive to talk about sets (of ordered pairs) $\displaystyle \mathrm{S}=\{(x,y)\in\mathbb{R}\times\mathbb{R}\mi d y=2x-1\}$. Then one could write like this $\displaystyle (a,b)\in\mathrm{S}$, which means by definition of $\displaystyle \mathrm{S}$ that $\displaystyle a$ and $\displaystyle b$ are real numbers, and $\displaystyle b=2a-1$. So instead of saying "consider expressions", try to say "consider a set(s)".

6. my answer was 'if and only if' as well, which seems logical. but it was wrong. how can you explain that?

7. Originally Posted by the kopite
my answer was 'if and only if' as well, which seems logical. but it was wrong. how can you explain that?