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discrete math set proof?
- Thread starter mgk501
- Start date
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.
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Hello, mgk501!
\(\displaystyle A\) 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: .\(\displaystyle A \,=\,B\)
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: .\(\displaystyle A \,=\,B\)