Welcome to the forum.

This is a wrong set-builder notation. For example, in A={x ∈ N:2x}, what is to the right of : must be a property that is either true or false for each x ∈ N, whereas you have a number there. If you mean A = {2x : x ∈ N}, B = {4x - 1 : x ∈ N} and C = {1}, then this is not a partition because 5 is not in A ∪ B ∪ C.1.Give an example of a partition of N into 3 subsets.

ANSWER: Let s={A,B,C) where A={x ∈ N:2x},B={x ∈ N:4x-1} and C={1}

It is true that ( is the set of integers); however, you are only asked to find . The intersection is not empty either.2.For a real # r, define S<subscript>r</subscript>to be the interval [r-1,r+2]. Let A={1,3,4}. Determine ∪∝∈A S∝ and ∩∝∈ A S∝

ANSWER: ∪∝∈A S∝=(-∞,∞) and ∩∝∈ A S∝=0(empty set)

We have . Also, .3.For a real number r, define A<subscript>r</subscript>={r^2}... For S={1,2,4}

a) ∪∝∈S A∝ and ∩∝∈ S A∝

A couple of remarks concerning notation. In plain text, it is customary to express subscripts and superscripts using _ and ^. If you want to typeset nice formulas, you can put text inside the [tex]...[/tex] tag. You can double-click on formulas in this post to see their source code, or you can click "Reply with code" to see the code for the whole post.

The symbol ∝ is usually used to denote some binary relations; it is strange to use it as a letter (like x or r).