1. Use mathematical induction to show that 2n < n! for all n ≥ 4. 2. Use strong induction to prove that every integer am
Posted: Mon Jul 11, 2022 12:46 pm
1. Use mathematical induction to show that2n < n! for all n≥ 4.
2. Use strong induction to prove that every integer amountof postage greater than 14 cents can be formed using only 3-centand 8-cent coins.
3. A chocolate bar consists of n squares arranged in arectangular pattern. The entire bar, or any smaller rectangularpiece of the bar, can be broken along a vertical or a horizontalline separating the squares. Prove using strong induction that itn−1 breaks are required to break a chocolate bar into n pieces.
4. Recursively define each of the following sets:
(a) The set of powers of 2.
(b) The set of integers congruent to 4 modulo 5.
(c) The set of bit-strings with an even number of 1’s
5. Recursively define a function f that takes as input abit-string and flips each of its bits. (e.g. f(1101) = 0010)
2. Use strong induction to prove that every integer amountof postage greater than 14 cents can be formed using only 3-centand 8-cent coins.
3. A chocolate bar consists of n squares arranged in arectangular pattern. The entire bar, or any smaller rectangularpiece of the bar, can be broken along a vertical or a horizontalline separating the squares. Prove using strong induction that itn−1 breaks are required to break a chocolate bar into n pieces.
4. Recursively define each of the following sets:
(a) The set of powers of 2.
(b) The set of integers congruent to 4 modulo 5.
(c) The set of bit-strings with an even number of 1’s
5. Recursively define a function f that takes as input abit-string and flips each of its bits. (e.g. f(1101) = 0010)