Let A be the set of all strings of 0’s, 1’s, and 2’s of length 4.

Define a relation R on A as follows:  For all s, t ∈ A,

    s R t ⇔ the sum of the characters in s equals the sum of the characters in t.

True or False: 2212 R 2121.

Let A be the set of all strings of a’s and b’s of length 4.

Define a relation R on A as follows: For all s, t ∈ A,

s R t ⇔ s has the same first two characters as t.

True or False: aaaa R aaab.

Define a function S: Z⁺ → Z⁺ as follows: For each positive integer n,

S = the sum of the positive divisors of n.

True or False: S(18) = S(32).

True or False: If two elements in the domain of a function are equal, then their images in the co-domain are equal.