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Define S, a set of bit strings, recursively as follows. Initial Condition:  0 ∈ S Recursion: If m ∈ S then 1m ∈ S. Which of the following best describes set S?  

For all positive integers a, b, c, and m with c > 0 and m > 1, if a ≡  b(mod cm), then a ≡ (c b)(mod m).

If a and b are integers and p is a prime number such that p | ab, then p | a or p | b.

Which of the following statements has a syntax error? Assume age and years are variables that have already been defined.

Write a program that displays the number of inches given feet as input. Create a function named main that is invoked within the same program. No comments are needed. Example 1 (your program must produce the same exact output given the input): Enter a whole number of feet: 1 12 inches Example 2 (your program must produce the same exact output given the input): Enter a whole number of feet: 2 24 inches

The function f : ℤ ⟶ ℤ defined by f(n) = n(mod 11) is a bijection.

Every integer > 1 has a unique prime factorization, with the prime factors written in non-decreasing order.

For arbitrary positive integers a, b, and c, with a ≠ 0, if a | (b c), then a | b and a | c.

If the universe of discourse for x and y is the set of positive real numbers, ∀x ∃y [ ( x2 + 1 ) y = 1 ]

For arbitrary integers a and b and arbitrary prime number p, if p | (a b) and p | a, then p | b.