Discrete Math. Check equality according to the laws of operations with sets

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Is the triangle symbol supposed to be the symmetric difference?

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I guess yes

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Draw a picture

That is a good enough proof

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What picture?

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Usually when you are to prove set theory things it is helpful to draw diagrams

Like so

Wait

Let me give an example

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I have to write

And compare then

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Or you can do that

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The left side is S1 and the right one S2

I tried but in result nothing

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Ok

What is the symmetric difference betwene 2 sets?

What is the definition

Answer this before you can continue

Understand every single term in the question

Before you can tackle it

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Okay

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Given 2 sets, A and B

What does A triangle B means?

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I have some formulas in my copybook

That's all I've got to use I suppose

I don't know if I can use other formulas

That are in internet

(the language on photo is Ukrainian)

And I found something like this

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Yes

THe symmetric difference of 2 sets it's just what they don't have in common,

( A \ B ) U ( B \ A )

[brazen plinth]

Hm

Can I show you what I wrote?

And you'll tell me if it's right

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Yes

Do that please

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What does that bar above means?

I never seen this notation before

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Ok

Let's seee

This is my proof

Yellow is A intersect B

Blue is A intersect C

So that means that their symmetric difference ( everything that they DON'T have in common )

So it's this

This last picutre symbolises the left hand side, S1 for you

Now let's try to see what we get when we do S2

This green is A\B

This brick color is A \ C

So their symmetric difference ( The thing that they DON'T have in common ) is this

Wait

So this

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So S1 = S2?

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Yes

That's all

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Hm

But there comes the hard part

I have to do it with formulas...

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It's the same thing

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Yes

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It's fine even you don't write it with formulas

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But the task is to write it

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You can just draw these diagrams what your though process and that's totally fine

But if you insist

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Because I have tasks to draw also

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This is S1

And probably do some other set operation manipulation

Idk

good luck

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+close