Final answer:
The set of whole numbers is closed under multiplication, always resulting in another whole number. It is not closed under division, as it can result in a fraction or decimal. The rules of signs in multiplication and division state that like signs yield a positive product or quotient, and unlike signs yield a negative result.
Step-by-step explanation:
The set of whole numbers is indeed closed under the operation of multiplication. This means that whenever you multiply two whole numbers together, the result is always another whole number. For example, when we multiply 2 by 3, the result is 6, which is also a whole number.
However, the set of whole numbers is not closed under the operation of division. In some cases, dividing one whole number by another can result in a fraction or decimal, which is not considered a whole number. For instance, if we divide 3 by 2, we get 1.5, which is not a whole number.
To review the rules of multiplication and division regarding signs, when we multiply or divide two positive numbers or two negative numbers, the result is positive (e.g., 2x3 = 6 or (-4) x (-3) = 12). If we multiply or divide numbers with opposite signs, the result is negative (e.g., (-3) x 2 = -6).