Basic Notation Help for Intro Economics Course: Calculus, Functions, and Sets"

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Homework Statement

In an intro Economics course, the teacher gave us some questions regarding function notation. I learned calculus to a decent level, but I have problems with notation.

Homework Equations

Question 1. Give an explicit expression for the following set: { x : x ∈ Z and x < 2 }
Question 2. Give an example of an element (y) of the following set: Y = Y1 x Y2 x Y3 , whereY1 = set of train engines = { green, blue, red }, Y2 =set of train cars = { passenger, boxcar, tanker }, Y3 = set of cabooses = { red }.
Question 3. Consider the function f : X → Y, when Y = R and f and X are defined as
follows: X = {(1,1,0), (1,0,1), (1,0,0), (0,1,0), (0,0,1)} and f (x) = x1 + x2 + 2x3. Now what is the set { x : f (x) = 2, x ∈ X }? (NOTE: It is not x*2 or 2x*3, but x with a little two beside it, 2x with a little three beside it).

The Attempt at a Solution

Question 1: I don't get what "explicit expression" means. It wants an integer less than two...
{x: (- infinity, 2), x ∈ Z}
Question 2: [Green, boxcar, red caboose]
Question 3: (1, 1, 0)

Can someone please tell me where/if I went wrong?

 

[LCKurtz]

Homework Statement

In an intro Economics course, the teacher gave us some questions regarding function notation. I learned calculus to a decent level, but I have problems with notation.

Homework Equations

Question 1. Give an explicit expression for the following set: { x : x ∈ Z and x < 2 }

Question 2. Give an example of an element (y) of the following set: Y = Y1 x Y2 x Y3 , whereY1 = set of train engines = { green, blue, red }, Y2 =set of train cars = { passenger, boxcar, tanker }, Y3 = set of cabooses = { red }.
Question 3. Consider the function f : X → Y, when Y = R and f and X are defined as
follows: X = {(1,1,0), (1,0,1), (1,0,0), (0,1,0), (0,0,1)} and f (x) = x1 + x2 + 2x3. Now what is the set { x : f (x) = 2, x ∈ X }? (NOTE: It is not x*2 or 2x*3, but x with a little two beside it, 2x with a little three beside it).

Those little numbers are called subscripts. You can use the X₂ icon to make subscripts. Apparently they are labelling the members of X like x₁=(1,1,0), x₂= (1,0,1), etc, using the subscripts as indices to label them.

The Attempt at a Solution

Question 1: I don't get what "explicit expression" means. It wants an integer less than two...
{x: (- infinity, 2), x ∈ Z}

It might mean {1,0,-1,-2,-3,...} where the ... means continue.

Question 2: [Green, boxcar, red caboose]

Usual notation would use ( ) instead of [ ].

Question 3: (1, 1, 0)

Add x₁, x₂ and 2x₃ in the usual way.