discrete math set proof?

[mgk501]

Need help w/ this problem please....also, what is z^+? Thanks

Show that A=B if A = {1,2,3} and B = {n | n ∈ Z^+ and n^2 <10}

 

[daon2]

Need help w/ this problem please....also, what is z^+? Thanks

Show that A=B if A = {1,2,3} and B = {n | n ∈ Z^+ and n^2 <10}

$\displaystyle \mathbb{Z}^+$ means the positive integers. You will need to show A is a subset of B and B is a subset of A.

A is a subset of B: Show that when you square an element of A, the resulting integer is less than 10.

B is a subset of A: Show that if the square of a positive integer is less than 10, then the integer must be one of 1, 2 or 3.

 

[soroban]

Hello, mgk501!

Need help w/ this problem please . . . also, what is $\displaystyle Z^+$ ? . The set of positive integers

Show that $\displaystyle A=B\,\text{ if }\,A = \{1,2,3\}\,\text{ and }\,B = \{n\,|\,n\in Z^+ \text{ and }n^2 <10\}$

$\displaystyle A$ contains the integers 1, 2, 3.


$\displaystyle B$ is a positive integer whose square is less than 10.

. . $\displaystyle \begin{array}{ccc}1^2 \:=\: 1 \\ 2^2 \:=\: 4 \\ 3^2 \:=\: 9 \\ \; \color{red}{\rlap{///////}}4^2 \:=\: 16 \\ \vdots \end{array}$

Hence, $\displaystyle B$ contains the integers 1, 2, 3.


Therefore: .$\displaystyle A \,=\,B$

 

[mgk501]

Awesome!! thank you both very much, I wasn't sure what that meant at first but it makes perfect sense now.