Question

Show that if A and B are sets then A\B= A and not B

Answer 1

really? isn't this just a set property?

Answer 2

I mean

Answer 3

intersect B complement?

Answer 4

\[A \backslash B = A \cap B^c\]

Answer 5

that's set property o-o

Answer 6

its in the definition.

Answer 7

isn't that the definition?

Answer 8

yeah... so taking the left \[A \backslash B\]
\[A \cap B^c\]

Answer 9

\[A \cap B^c = A \cap B^c\]

Answer 10

oops forgot to mention by set property then we have it equal can't just do symbolz

Answer 11

\[
A\setminus B = \{x|x\in A\land x\notin B \} = A\cap B^C
\]

Answer 12

qedgmc

Answer 13

yeah it's from another book... somehow I understand their material better ... I'm just trying to find the inverse function and the injection surjection stuff from it

Answer 14

\[(B \backslash A) \cup (C \backslash A) = (B \cup C) \backslash A\]

Answer 15

I'm just using distributive law to take the \A out

Answer 16

\[(B \cup C) \backslash A\] for the left via distributive law

Answer 17

is this the same problem?

Answer 18

and then if I start form the right... I would apply the distributive law to get from \[(B \cup C) \backslash A \] to \[(B \backslash A) \cup (C \backslash ) \]

Answer 19

:O where it go?!

Answer 20

no different

Answer 21

\[(B \backslash A) \cup (C \backslash A )\]

Answer 22

do you know induction that involves factorials?