Question

Let A, B, and C be sets. Prove that if A is not a subset of C, then A is not a subset of B or B is not a subset of C.

Answer 1

assume A is not a subset of C
suppose A is a subset of B
then every element of A is in B, but not every element of A is in C
so B has some element (from A) that is not in C
so B is not a subset of C

since A is either a subset of B or not a subset of B, the proof is complete.

Answer 2

I would write it more formally but the text editor is having problems with latex...

Answer 3

do you understand?

Answer 4

Kinda! So you're saying that a similar argument can be made for A not a subset of B that you made for A subset of B?

Answer 5

well we need to prove an "or" statement
so all we need is either one or the other

i showed
given that A is not a subset of C
then A is a subset of B implies B is not a subset of C

now we have shown that if A is a subset of B then B is not a ss of C
but if we assume the contrary ( A is not a subset of B)
then there is nothing to prove because we are proving A is not a subset of B OR B is not a subset of C

Answer 6

we have
\[a\implies\text{ b or c}\]we showed that given a
we assume ~b and we get c

Answer 7

Oh okay, that makes a lot of sense! Thank you so much! I forgot about the 'or' lol...but thank you!

Answer 8

so if we have ~b we need to show that we have c because its an or statement
and if we have b we do not need to show c because its an or statement

Answer 9

np