Explanation:
The statement you provided is a conditional statement: "If a * b = 0, then either a = 0 or b = 0."
The inverse of this statement would be: "If a * b ≠ 0, then both a ≠ 0 and b ≠ 0."
This inverse statement essentially flips the original statement and negates both the hypothesis and the conclusion.
The converse of the statement would be: "If either a = 0 or b = 0, then a * b = 0."
The converse statement swaps the hypothesis and the conclusion of the original statement.
The contrapositive of the statement would be: "If a * b ≠ 0, then both a ≠ 0 and b ≠ 0."
The contrapositive statement is the inverse of the converse, which flips and negates both the hypothesis and conclusion of the converse statement.
It's important to note that while the original statement is true, the other three (inverse, converse, and contrapositive) statements may or may not be true. In some cases, they might be true, but in others, they could be false.