Question

Proof:
Let A be an event. Then ∅ ⊂ A

help by elucidating

Answer 1

Let A an arbitrary event, and since an empty set indicate no points, it is sound to point out that every point belonging to ∅ belongs to A

Answer 2

the empty set is a subset of every set
vacuously so as \(A\subset B\iff x\in A\implies x\in B\)

Answer 3

that's the kind of notation I am looking for!
thank you @satellite73

Answer 4

that is basically saying that the empty set is a subset of the event A
The empty set is a subset of all sets

Answer 5

you know how to check it right? i mean the \(\LaTeX\)

Answer 6

I am a TEX newbie

Answer 7

\[A\subset B\iff\forall x, x\in A\implies x\in B\] would be more precise

Answer 8

right click and check what you need

Answer 9

Yes that is the definition of a subset. Every element that is in A is also in B ^

Answer 10

thanks also, @Miracrown

Answer 11

i did nothing tho

Answer 12

you participated LOL that's good enough

Answer 13

sureeee.... I was under the impression that the empty set was defined to be a subset of all sets. I am not really sure how to prove it
A set with no elements is essentially a subset of any set because no element is also part of any other set

Answer 14

it is because of the definition that starts with IF \(x\in A\)

Answer 15

Ok, since x is not an element of the empty set, then that is by default false, and any implication that starts with F is by default true

Answer 16

spanks!