Discrete Math: defining sets, drawing Venn diagrams, sorting teams, defining fcns

[Plonker]

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

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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

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a) You can see my drawing attempt, sorry for the messiness. 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?

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3&4 I have no idea how to do.

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

 

[MancPaul]

First things first

Your very first answer is incorrect. Whilst it is true that 2,4 and 6 belong to the set of even numbers less than 15 it is not true that {2,4,6} is and element of this set. {2,4,6} is a set not an even number less than 15

I hope this is understood

 

[stapel]

< link removed >

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

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a) True, all elements of E are even
b) False, 0 is not a multiple of 3

Zero is a multiple of everything. In this case, 0*3 = 0.

c) True, 8 is even and 9 is a multiple of 3

How are you getting that ordered pairs, elements of none of the initial sets, are elements of the unions of two of those sets?

d) No idea

What do you mean by this? Which part is confusing to you?

e) False, 6 is an element of E and T

You are correct that the statement is false, and your counter-example (the number 6) is how you correctly justify your answer.d

f) No idea

How does your book define this notation?

Please be complete. Thank you!

 

[HallsofIvy]

Zero is a multiple of everything. In this case, 0*3 = 0.

But 0 is not in N.

 

[JeffM]

But 0 is not in N.

Context is all.

The OP said, in answer to a question requiring justification, that 0 is not in the intersection of U and T BECAUSE 0 is not a multiple of 3. That justification was clearly wrong because, as pointed out by stapel, 0 is a multiple of three.

This raises the question of how to respond when a student gives an answer that may or may not be correct for a clearly incorrect reason. Few of us always give perfect responses. Upon reflection, I guess a perfect response might have been along the lines "FALSE may or may not be the correct answer, but your justification is certainly incorrect. 0 is most certainly a multiple of 3 (as is every other number). How does your book define N? Why is that definition relevant?"

Without knowing how that text defines N, we do not know the correct answer ourselves. The problem warns of traps.