3rd one

[lean ivy]

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[fickle wraith]

Alright, consider the diagonal set $\Delta:={(x,x), x \in {1,…,n} }$

[boreal hinge]

Rotator

[fickle wraith]

then you are trying to find the number of elements of ${B \subset A: \Delta \subset B }$

Do you agree ?

[boreal hinge]

Rotator

[woeful oriole]

sorry, i got busy w something

[woeful oriole]

This was my approach towards ths question when i first read it.

Where did i make the mistake

What did i misunderstand in ths question

[fickle wraith]

A is S x S, not {(1,1),(2,2),…,(n,n)}

[fickle wraith]

I named this set Delta here

[fickle wraith]

A has n^2 elements so the number of subsets of A is 2^n^2

[woeful oriole]

Oh, so basically a=b so u let it a,a or x,x?

[fickle wraith]

Here you are trying to find the number of subsets of A that contain Delta

[fickle wraith]

A is {(a,b) for 1<=a <=n and 1<=b<=n}

a and b can be different

for example if n=2 then (1,2) is in A

[woeful oriole]

Ahh

[fickle wraith]

but here Delta is {(1,1),..,(n,n)}

[woeful oriole]

I get it

[fickle wraith]

Si a=b

*so

[fickle wraith]

Yeah so you are trying to find this

Now I ask you this: on what condition on the complement does a subset of A contain Delta ?

[woeful oriole]

Uhh idk T_T

[fickle wraith]

if $\Delta \subset B$ then what can you say of $B^{c}$

[boreal hinge]

Rotator

[fickle wraith]

Here B^c is the complement of B in A

[woeful oriole]

Could u just solve it on paper? It will be easy for me to understand thn;-;

[fickle wraith]

You can say that $B^{c} \subset \Delta^{c}$

[boreal hinge]

Rotator

[fickle wraith]

do you agree ? @woeful oriole

If you take a subset B containing Delta then it’s complement must be a subset of the complement of Delta

[wooden pebble]

Some ppl just remember the formulas

But anyways you could learn the concept too

[fickle wraith]

So the subsets you are looking for are exactly complements (in A) of subsets of Delta^{c}

And this is one to one

now here is the question : how many subsets does Delta^c have ?

Instead of computing the number explicitly you can also proceed by elimination

it can’t be (A) or (D) for simple reasons

So it’s either (B) or (C)