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.

The great mathematician Countalot discovered the Incrediblenumbers; he does not know yet if they are finite or infinite,but he made the following conjecture:If they are infinite, then at least one of them has 8 distinctprime factors.One of his students, Countagain, showed that Countalot’sconjecture is false. Therefore he proved that:A. if Incredible numbers are finite, then none of them has 8distinct prime factorsB. if Incredible numbers are finite, then all of them have 8distinct prime factorsC. Incredible numbers are infiniteD. Incredible numbers are infinite and none of them has 8distinct prime factorsE. Incredible numbers are infinite and all of them have 8distinct prime factors22

Let A and B are positive number and composite number respectively. Then which of the following can be true None𝐴+𝐵𝐴𝐴+𝐵𝐴cannot be  an even integerB – A cannot be a even integerAB cannot be a even integer

All the following are true for irrational numbers except ...*1 pointthey have repeating decimalsthey are square root of prime numbersthey have nonterminating decimalsthey are square root of composite numbers without perfert squareOther:

Make a conjecture for each scenario. Show your work. 3. the square of an even number 4. the product of two odd numbers and a multiple of 2 Find one counterexample to show that each conjecture is false. 5. For two real numbers a and b, a is either equal to b or greater than b. 6. All quadrilaterals are parallelograms.

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.