Intro to abstract math—basic notation

[TyroneTheDino]

Homework Statement

Simplify the following statement as much as you can:

(b).
$(3<4) \wedge (3<6)$

Homework Equations

$\wedge= and$

The Attempt at a Solution

I figured that I could just write this as $3<4<6$,
but then I considered what if I didn't know that $4<6$
If it was just $(3<x)\wedge (3<y)$, then I would have to consider that I don't know either x or y.
Is it okay to say that $3<4<6$ though I just assume that $4<6$?
Or is statement already simplified enough.
Is $3<4, 6$ a way to get around this?

 

[Mark44]

Homework Statement

Simplify the following statement as much as you can:

(b).
$(3<4) \wedge (3<6)$

Homework Equations

$\wedge= and$

The Attempt at a Solution

I figured that I could just write this as $3<4<6$,

If 3 < 4, then 3 is automatically smaller than 6, so that latter statement is redundant.

but then I considered what if I didn't know that $4<6$

You know how to count to 10, right? Then you know that 4 < 6.

If it was just $(3<x)\wedge (3<y)$, then I would have to consider that I don't know either x or y.
Is it okay to say that $3<4<6$ though I just assume that $4<6$?
Or is statement already simplified enough.
Is $3<4, 6$ a way to get around this?

No, 3 < 4, 6 is not any sort of standard notation.

 

[HallsofIvy]

I would not say "3< 4< 6" because "3 is less than 4 and 3 is less than 6" does NOT, as you say, say that "4< 6". I think the most "simplified" form is just what I said before: "3 is less than 4 and 3 is less than 6" or perhaps "3 is less that either 4 or 6". If you take it as given that 4< 6 then "3< 4 and 3< 6" is equivalent to "3< 4" since then "3< 6" follows immediately.

 

[Fredrik]

Are you allowed to replace a statement with a symbol that means "true"? The number 1 is often used for that purpose. (0 is used for "false").

If the problem had asked you to simplify $\{x\in\mathbb R|(x<4)\land(x<6)\}$, I would have said $\{x\in\mathbb R|x<4\}$. (Since 4<6, the statements "x<4" and "x<4 and x<6") are equivalent for all real numbers x). But here I don't think it makes sense to use that 4<6.

The problem is kind of weird. It might help if you tell us where you found it.