question 72 question 70 b Use the second principle of on the

question 72?

question 70?

b. Use the second principle of on the number of subwords in the word) to prove that any word language has an even number of o\'s 72. A simple closed polygon consists of n points in the plane joined in pairs by n line segments; each point is the endpoint of exactly 2 line segments. Following are two examples. a. Use the first principle of induction to prove that the sum of the interior angles of an n-sided simple closed polygon is (n 201800 for a n 2 3. b, Use the second principle of induction to prove that the sum of the interior angles of an n-sided simple closed polygon is (n 2)180 for all n 2 3. 73, The Computer Science club is sponsoring a jigsaw puzzle contest. Jigsaw puzzles are assembled by fitting 2 pieces together to form a small block, adding a single piece to a block to form a bigger block, or fitting

Solution

Question 70:

In the given induction proof of the problem, base condition is defined correctly. but the recursive definition of the induction is not true. Because the assumption on which this proof deduces the logic that all the other computer in P(k+1) are of same manufacturer. you cannot come to a conclusion like that, because there may be a possibility of a computer named HAL to be of other manufacturer than the one which is concluded. So if the conclusion is deduced by the definition like P(2) is also a computer named HAL from same manufacturer and P(3) and so on. then only we can conclude. Please notice that there is one more possibility of a manufacturer producing more than one type or name of a computer. then this syllogism is also holds untrue for the given induction proof to prove that all computers are built from same manufacturer.