Pls check if these are correct. 1) If the following statement true or false? Explain your reasoning. All integers are rational numbers. (1 pt.) - The statement is false because 0 is an integer but cannot be written as the ratio of two integers - The statement is true because all numbers are rational numbers ✅ The statement is true because any integer x can be written in the for x/1, which is the ratio of two integers - The statement is false because 1/2 is a rational number but not an integer 2) Which of the following must describe an irrational number?(1 point) ✅ A number with a non repeating and non terminating decimal expansion - A number with a non terminating decimal expansion - A number with a non repeating decimal expansion - A number with a repeating or terminating decimal expansion 3)Which axiom is used to prove that the product of two rational numbers is rational?(1 point) - Natural numbers are closed under multiplication - Whole numbers are closed under division ✅ Integers are closed under multiplication - Integers are closed under division 4) Without calculating, how do you know the product 2/21 x 3/31 is rational? (1 point) - The product of any two positive numbers is rational. - When multiplying fractions, the product of two fractions is rational so long as both fractions are less than 1. ✅ Rational numbers are closed under multiplication, meaning that the product of rational numbers is rational. - When multiplying fractions. the product of two fractions is rational so long as both fractions are fully reduced 5) What rational number, when multiplied by an irrational number, has a product that is a rational number? (1 point) ✅ 1/2 - 1/10 - 0 - 1 Thx if you help