- #1

karush

Gold Member

MHB

- 3,269

- 5

Let $H=\{0;\pm 3;\pm 6;\pm 9;\cdots\}$.

$\textit{ Use }$

$$aH=bH \textit{ or }aH\cap bH=\oslash$$

$\textit{then..}$

$$aH = bH \textit{ iff } (b-a) \textit{ is in } \textit{H}$$

to decide whether or not the following cosets of H are the same.

$\textsf{a. 11 + H and 17 + H}$

$\textsf{b. -1 + H and 5 + H}$

$\textsf{c. 7 + H and 23 + H}$ok not sure what the official method of this would be but for a. 11+6=17 so the coset would would be just a shift over 6 places. the same shift seens to be true for b and c however the beginning numbers would be different

however the book says that c is no

$\textit{ Use }$

$$aH=bH \textit{ or }aH\cap bH=\oslash$$

$\textit{then..}$

$$aH = bH \textit{ iff } (b-a) \textit{ is in } \textit{H}$$

to decide whether or not the following cosets of H are the same.

$\textsf{a. 11 + H and 17 + H}$

$\textsf{b. -1 + H and 5 + H}$

$\textsf{c. 7 + H and 23 + H}$ok not sure what the official method of this would be but for a. 11+6=17 so the coset would would be just a shift over 6 places. the same shift seens to be true for b and c however the beginning numbers would be different

however the book says that c is no

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