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

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Advance Math

A binary string is a “word” in which each “letter” can only be 0or 1
Prove that there are 2^n different binary strings of lengthn.
Note:
Your goal is to produce a properly constructed proof byinduction, 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=kversion of the statement is true, and using thisassumption to prove that the n=k+1 version of thestatement 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 are2ⁿ different binary strings of lengthn” !!! So your solution should primarily be discussingbinary strings. Yes, the fact that2^k⁺¹ = 2^k?2 willbe useful in your solution, but it should not be the sole contentof your solution, as by itself that equality is a fact aboutexponents, not a fact about binary strings.

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Step 1 Basic step for n 1 we can easily see that there are 2 ways to choose the letters 0 and 1 Therefore the number of ways a word of length 1 can be written is 21 See Answer

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