Answer:
Explanation:
To have the product of three integers be negative, we must have an odd number of negative integers. This is because when two negative integers are multiplied, the result is positive, and when an odd number of negative integers are multiplied, the result is negative. Therefore, we need at least one negative integer to produce a negative product, and then either one or three negative integers depending on whether the other two integers are positive or negative.
Here are two groups of three integers whose product is negative:
Group 1: {-1, 2, 3}
Product = (-1) x 2 x 3 = -6
In this group, there is one negative integer and two positive integers, which gives us an odd number of negative integers and a negative product.
Group 2: {-2, -3, 4}
Product = (-2) x (-3) x 4 = 24
In this group, there are two negative integers and one positive integer, which gives us an even number of negative integers and a positive product.
Note that there are infinitely many groups of three integers that can produce a negative product, as long as there is an odd number of negative integers in the group.