Question

A binary string is a “word” in which each “letter” can only be 0 or 1

Prove that there are 2^n different binary strings of length n.

Note:

• Your goal is to produce a properly constructed proof by induction, but this does not mean you have to follow
• Mathematical induction, step-by-step..
• Write the statement with n replaced by k
• Write the statement with n replaced by k+1.
• Identify the connection between the kth statement and the (k+1)th statement.
• Complete the induction step by assuming that the n=k version of the statement is true, and using this assumption to prove that the n=k+1 version of the statement is true.
• Complete the induction proof by proving the base case.
• point-by-point.
• ANOTHER IMPORTANT NOTE:
• Make sure you are addressing the given statement: "there are 2ⁿ different binary strings of length n” !!! So your solution should primarily be discussing binary strings. Yes, the fact that 2^k+1 = 2^k∙2 will be useful in your solution, but it should not be the sole content of your solution, as by itself that equality is a fact about exponents, not a fact about binary strings.

Answer 1