Determine whether the proposed negation is correct. If it is not, write a correct negation. Statement: The product of any irrational number and any rational number is irrational. Proposed negation: The product of any irrational number and any rational number is rational. The proposed negation is correct. The proposed negation is not correct. A possible correct negation would be: There is an irrational number and a rational number whose product is rational. The proposed negation is not correct. A possible correct negation would be: There is not an irrational number and a rational number whose product is rational. The proposed negation is not correct. A possible correct negation would be: There exists an irrational product of an irrational number and a rational number. The proposed negation is not correct. A possible correct negation would be: There does not exist an irrational product of any irrational number and any rational number.

Prove or disprove: The sum of any two irrational numbers is irrational. Either give a general proof of this statement or give a counter-example.

discrete math: Give the negations of the following statements.  Determine the truth value of each statement. Every integer is even or odd.                                                            T / F Negation_______________________________________________________         T / F   Every real number is positive or negative.                                         T / F Negation___________________________________________________         T / F   Some people don’t like discrete math.                                                   T / F Negation___________________________________________________         T / F

Write the negation of of the following statement: “For every pair of real numbers x and y if x < y, then there exists a rational number q such that x < q < y.”