Question

what is meant by the negation of a proposition? make up an example of a proposition and its negation. what is meant by the negation of a proposition? if p is a proposition, then the negation of p is if p is true, then the negation of p is if p is false, then the negation of p is make up an example of a proposition and its negation. choose the correct answer below. a. given the proposition \the product of two negative numbers is a positive number,\ the negation would be \the product of two positive numbers is a negative number\ b. given the proposition \the product of two positive numbers is a positive number,\ the negation would be \the product of two positive numbers is not a negative number.\ c. given the proposition \the product of two negative numbers is a negative number,\ the negation would be \the product of two positive numbers is a positive number.\ d. given the proposition \the product of two negative numbers is a positive number,\ the negation would be \the product of two negative numbers is not a positive number.\

Explanation:

The negation of a proposition \(p\) is a statement that has the opposite truth - value of \(p\). If \(p\) is true, its negation is false and if \(p\) is false, its negation is true. To find the negation of a statement, we change the truth - value of the statement. In option D, the original proposition "The product of two negative numbers is a positive number" is a true statement. Its negation "The product of two negative numbers is not a positive number" has the opposite truth - value.

Answer:

D. Given the proposition "The product of two negative numbers is a positive number," the negation would be "The product of two negative numbers is not a positive number."