Hello everyone, can someone please help me with the set theory question
(AB)C =A(BC)
I did a Venn diagram and I see that they’re not the same and now I need to do a proof by counter example. Any ideas where and how would do I start and do a set up for that?
Thank you
In: 2
Let x be in A and C, but not in B.
Then x is not in (AB)C because x is in C.
But x is in A, and not in B. Thus x is in A(BC).
What part of your Venn diagram is different?
Then write, suppose x is in … (That part of the Venn diagram).
Then show that x is not in the other side.
If you want a practical case:
A = Men
B = Peoples with blond hairs
C = Peoples with blue eyes
(AB)C = Men with no blond hairs and no blue eyes either.
A(BC) = Men with no blond hairs except if they have blue eyes in which case it’s ok for them to have blond hairs too.
So if you take MCU’s Thor (Christopher Hemsworth), then he is not in the first one but is in the second one.
Latest Answers