Math Is Fun Forum

Ffahim

Member

Registered: 2016-06-20

Posts: 2

Set problem of proving equation.

How to proof that A u A' = U  and if A intersection B ={} then how A is subset of B'?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Set problem of proving equation.

hi Ffahim

Welcome to the forum.

You would have to go back to basic definitions:

The Union of two sets means all elments in one set OR the other, so

If

Suppose

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Set problem of proving equation.

Hi Bob,

You can superscript the "\prime" to have it look like normal, like so:

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Ffahim

Member

Registered: 2016-06-20

Posts: 2

Re: Set problem of proving equation.

Thanks both of u for ur help. Now can u pls tell me that here are two sets each having 3 elements. Let's say set A={1,2,3} and B={x,y,z}. I have to show one one correspondence. Now how I would figure out that how many way I can show one one correspondence.?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Set problem of proving equation.

hi Ffahim

To show a 1:1 correspondence between two sets of the same size is is only necessary to create an equivalence relation between them eg.:  A ~ 1   B ~ 3 and C ~ 2, where ~ means "is equivalent to".

How many ways could you do this?

Well A must be related to either 1, or 2, or 3; so that makes 3 ways so far.

Then B must be related to one of the remaining numbers; two ways for that.

C must then be related to the single remaining number; just one way for that.

Total number of ways: 3 x 2 x 1 = 6

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob