MATH1061/7861, Mon 7 Sep 2020
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Question 1. x ◦ Is 4 ∈ {4} ? Is 4 ⊆ {4} ?
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◦ Is 4 ∈ {{4}} ? Is 4 ⊆ {{4}} ?
◦ Is {4} ∈ {2,3,4} ? Is {4} ⊆ {2,3,4} ?
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Question 2. Let D = {n ∈ N | n ≡ 2 (mod 8)}, and let E be the set of even integers. Prove that D ⊆ E.
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Question 5. The Tower of Hanoi: Let Ti denote the smallest number of moves required for i discs.
◦ Compute T0, T1, T2 and T3.
◦ Write a recurrence relation for the sequence {Ti}. ◦ Prove your recurrence relation correct!
◦ Guess an explicit formula for the Ti.
◦ Prove your explicit formula correct!
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