Which one of the following is FALSE about COLLATZ conjecture?*1 pointIf n is odd then multiply by 3 and then add 1 to it.After some iterations the number n will become 1If n is even then divide by 2We can calculate the number of iteration after which the number will become 1

The Collatz Conjecture, also known as the 3n + 1 problem, is a conjecture in number theory, first proposed by Lothar Collatz in 1937. The conjecture is as follows:Start with any positive integer 𝑛n. If 𝑛n is even, divide it by 2. If 𝑛n is odd, triple it and add 1. Repeat this process indefinitely. The conjecture states that no matter what value of 𝑛n you start with, you will always eventually reach the cycle 4,2,14,2,1.For example, starting with 𝑛=7n=7, the sequence is 7,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,17,22,11,34,17,52,26,13,40,20,10,5,16,8,4,2,1.The Collatz Conjecture remains unproven, despite extensive computational verification for extremely large numbers. It is considered one of the most perplexing and enduring unsolved problems in mathematics. So, if you're up for a real challenge, attempting to prove or disprove the Collatz Conjecture could be an exciting purs

ScenarioIn 1937, a German mathematician named Lothar Collatz formulated an intriguing hypothesis (it still remains unproven) which can be described in the following way:take any non-negative and non-zero integer number and name it c0;if it's even, evaluate a new c0 as c0 ÷ 2;otherwise, if it's odd, evaluate a new c0 as 3 × c0 + 1;if c0 ≠ 1, go back to point 2.The hypothesis says that regardless of the initial value of c0, it will always go to 1.Of course, it's an extremely complex task to use a computer in order to prove the hypothesis for any natural number (it may even require artificial intelligence), but you can use Python to check some individual numbers. Maybe you'll even find the one which would disprove the hypothesis.Write a program which reads one natural number and executes the above steps as long as c0 remains different from 1. We also want you to count the steps needed to achieve the goal. Your code should output all the intermediate values of c0, too.Hint: the most important part of the problem is how to transform Collatz's idea into a while loop – this is the key to success.

Sort these conjectures into "always true", "sometimes true" and "never true".always true sometimes true never trueA prime number has an even number of factors. The sum of two consecutive numbers is a multiple of 2. A square number has an even number of factors.

For each of the following statements, either prove that the statement is true, or finda counterexample to show that the statement is false and explain your reasoning.(a) For each integer n, n is even if and only if 6n + 4 is even.(b) For all integers ℓ, m, n, if ℓ + m is odd and ℓ + n is even, then m + n is odd.

Given:(1) If n is an even number, then 5n + 2 is always an even number.(2) If n is an integer larger than 1, then 2^n − 1 is always a prime number.Select one of the following choices:Question 16Answera.(1) and (2) are True.b.(1) is True and (2) is False.c.(1) and (2) are False.d.(1) is False and (2) is True.