Let A, B, C, D, E ⊆ Z be defined as follows:A = {2n|n ∈ Z} —that is, A is the set of all (...

Let A, B, C, D, E ⊆ Z be defined as follows:

A = {2n|n ∈ Z} —that is, A is the set of all (integer) multiples of 2;

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B = {3n|n ∈ Z};

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C = {4n|n ∈ Z};

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D = {6n|n ∈ Z}; and

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E = {8n|n ∈ Z};

a) Which of the following statements are true and which are false?

i) E ⊆ C ⊆ A

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ii) A ⊆ C ⊆ E

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iii) B ⊆ D

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iv) D ⊆ B

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v) D ⊆ A

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vi)

b) Determine each of the following sets.

i) C ∩ E

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ii) B ∪ D

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iii) A ∩ B

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iv) B ∩ D

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v)

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vi) A ∩ E