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◦ Find a partition of Z with finitely many parts, each of which is infinitely large. ◦ Find a partition of Z with infinitely many parts, each of which is finite in size.
◦ Find a partition of Z with finitely many parts, each of which is finite in size. x
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◦ Find a partition of Z with infinitely many parts, each of which is infinitely large.
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Question 5. Prove that, for all sets A and B in some universe U, if A ⊆ B then B^∁ ⊆ A^∁.
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Question 6. Prove that, for all sets A and B, A − (A − B) = A ∩ B.
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Question 7. Prove that, for all sets A and B, A − (A ∩ B) = A − B.
Question 8. Let f :Z→Zbe the function f(x) = (x + 1)2. ◦ What is the image of 1?
◦ What is the image of {1}?
◦ What is the image of {1,2}?
◦ What is the domain?
◦ What is the codomain?
◦ What is the range?
◦ What is the preimage of 1?
◦ What is the preimage of 2?
◦ What is the preimage of {0,1,2}?
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