Understanding Sets, Relations, and Functions for Struggling Students

[Plonker1]

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I'm having issues with the first four questions and have uploaded them. My attempts are shown below.

1.
a) True, all elements of E are even
b) False, 0 is not a multiple of 3
c) True, 8 is even and 9 is a multiple of 3
d) No idea
e) False, 6 is an element of E and T
f) No idea

2.
a) You can see my drawing attempt on imgur, sorry for the messiness (ed's note: see below). The parts meant to be coloured in are in black.
b) This claim is false
c) I drew up another graph that I guessed proves it is false. Am I correct?

3&4 I have no idea how to do.

Thank you so much for any help,
A struggling student.
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[joypav]

I will comment on a couple things, but are you including 0 in your definition of the natural numbers?
Meaning, do you define the natural numbers as
N = {0,1,2,...} or N = {1,2,...}

Some people include 0 and some do not.