You have the symbolic notation confused.
If then prove that .
Start by picking a point , by definition .
Now can you finish be concluding that ?
Next start with pick .
We know that . Can you finish by showing ?
Prove the following:
Let and be sets. Then iff .
Here is what I am thinking, but I'm pretty sure there is some serious problems:
Let and be sets.
First Direction: Assume . Let . Since . Since . Because . Since .
Second Direction: Assume . Let . Since . Since . Since . Since and .
Need some help please. Thanks.
Okay, let's see what I can do here.
First way.
Assume .
Let .
Thus .
Since .
Because .
Hence, if , then .
Second way.
Assume .
Let .
Thus, {x} .
Since {x} .
Since .
Since , {x} .
Because {x} .
Hence, if .
Is this okay? Or did I do something wrong again? I'm pretty confused.