Let S be the set of all strings in a’s and b’s, and define C: S → S by C(s) = as, for all s ∈ S.

(C is called concatenation by a on the left.)

a. Is C one-to-one? Prove or give a counterexample.

b. Is C onto? Prove or give a counterexample.

Discrete Mathematics CS225 Terms and concepts: Week 2 Reading 145-159, 165-167. 183-184. 201-203 and Lectures and Supplemental Info List of Types of Numbers: • Natural numbers ( ℕ ): Counting numbers. {0, 1, 2, 3…} • Integers ( ℤ ): Positive and negative counting numbers. {…-2, -1, 0, 1, 2, …} • Rational numbers ( ℚ ): Numbers that can be expressed as a ratio of...