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Define S, a set of bit strings, recursively as follows. Initial Condition:  1 ∈ S Recursion: If m ∈ S then m11 ∈ S. Which of the following best describes set S?

According to Fermat’s little theorem, what is the value of 3374(mod 11)?

[1] The assignments and tests are good measures of how much I’m learning.

The octal expansion of the decimal number 109 is ___________eight. Only type the digits; do not include the base.

The pet shop in Mochdewton sells only guinea pigs and hamsters. Each guinea pig costs twice as much as a hamster. A local elementary school purchased 5 guinea pigs and 3 hamsters. If the transaction had been for 3 guinea pigs and 5 hamsters, the cost would have been $10 less. What is the price of a guinea pig?  [GuineaPig] What is the price of a hamster?   [Hamster]   Adapted from “The Lady or the Tiger? and other logic puzzles” by Raymond M. Smullyan

The binary expansion of the decimal number 105 is ___________two. Only type the digits; do not include the base.

To complete the division algorithm equation, a = mq + r, using a = – 38 and m = 7, which of the following gives appropriate values for integers q and r, with r expressed as a non-negative integer between 0 and (m-1), inclusive.

For arbitrary integers a, b, and d, with d ≠ 0, if there are integers s and t such that d = as + bt, then d = GCD(a, b).

Determine which of these set identities are supported by the entries in the membership table given below.  There may be more than one or none. Select ‘True’ if the identity is supported by this given membership table; otherwise select ‘False’. [1]  (A – B) – C ⊈ (A – B) [2]  (A – C) – B ⊂ (A – C) [3]  (A – B) ⊄ (A – C) – B [4]  (A – C) ≠ (A – B) – C [5]  (A – C) ⊆ (A – B) [6]  (A – C) – B = (A – B) – C A B C A – C A – B (A – C) – B (A – B) – C 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 1 0 1 0 0 1 1 0 1 0 0 0 1 1 1 0 0 0 0

Use the Euclidean algorithm to determine the GCD(286, 273).  Show your work. Then express the GCD(286, 273) value you identify as a linear combination of 286 and 273.  Show your work.