Question

A = { 1, 2, 3 }, B = { n | n is a positive integer and n^2 < 10 }. Show that A = B.

I can see it, but how am I supposed to show it..?

Answer 1

You can do something like: "Let \(n\) be a positive integer. Then, if \(n=1\), it follows that \(n^2=1\), which is less than \(10\). If \(n=2\), it follows that \(n^2=4\), which is less than \(10\). Etc."

Answer 2

Is that an acceptable form of proof in discrete math..? generally?

Answer 3

show that \(A\subseteq B\)

let \(x\in A\) then \(x=1,2\) or \(3\).
Surely \(0<1^2<2^2<3^2<10 \)
So \(A\subseteq B\)

Now \(B\subseteq A\)
Let \(x\in B\) then \(0<x^2<10\implies 0<x<\sqrt{10}\) or \(0>x>-\sqrt{10}\)
Since \(x\in \mathbb{N}\) we have \(x=1,2,\) or \(3\).
So \(B\subseteq A\).
Thus \(A=B \ \ \ \ \ _\square\)

Answer 4

First thing to do when showing to sets are equal is to show that one is a subset of the other, and then show the other way.

Answer 5

Does this make sense @calyne ?

Answer 6

Yes yes thank you!!