Did you plug that answer in to check it?

]]>If the statement is a tautology, give a proof using the appropriate rules of logic and avoid using truth tables if possible. If it is not a tautology, then justify your answer by giving an appropriate example.

This is from a course on logic so we are entitled to apply that exactly as stated. If a tautology don't use a table. But it isn't. So we must justify by example.

Certainly you wouldn't want me to prove anything that is false. A single counter-example is sufficient. I can get it by any method I like.

Bob

]]>That’s pretty useless to us. What we need is more than that: we need to show

In order to do that we show

I'm having a lot of difficulty making sense of the question.

she remembers that in 1961 she needed $3 more for each £1

More than what?

she is now receiving £40 more for each $100 exchanged

Again, more than what?

Here's my attempt to make an equation.

If the exchange rate is $d for £1 then $100 will become £(100/d)

In 1961 it took $3 more to get a £ so the exchange rate would be $(d+3) to make one £1. So $100 got £ 100/(d+3) in 1961.

So if she is now receiving £40 more that means 100/d = 100/(d+3) + 40

=> 100(d+3) = 100d + 40d(d+3)

This will simplify to the required equation.

Hope that helps.

Bob

]]>]]>

Teamwork!

Bob

]]>hi Dawn0388

Welcome to the forum.

The x-y system of coordinates was invented by the mathematician Descartes.

http://mathworld.wolfram.com/CartesianCoordinates.html

But you don't have to use x and y at all. For example to draw a graph of velocity changes with time, you might have 't' across and 'v' up.

You'll find more about coordinates at

http://www.mathsisfun.com/data/cartesia … nates.html

Bob

Thank you for answering me the question!

]]>The expression can be expanded easily at Wolfram alpha. Go here:

and enter in the input box,

(2/5 + x/4 + (15 x^2)/100 + x^3/10 + x^4/20 + x^5/20)^6

]]>This is definitely not the case in the diagram above (there are infinitely many non-straight lines, where each one of them has length X=1).

So, I still do not understand how 2*(a+b+c+d+...)=X by your string of notations.

Moreover, if length X=1 is defined in terms of the set of all **R** members in [0,1], and [0,1] is invariant (exactly as X=1 is invariant in the diagram above), then how exactly |**R**| is collapsed into cardinality 1 (which is the cardinality of the set with a single member (the vertex at the bottom of the big triangle))?

Yes, those answers look good to me.

Bob

]]>I want to show that:

That's what I have tried:

When

, it means that:So that

So,

.Is it right so far? Also, how can I show that

?]]>