4. Suppose that there are nine students in a discrete mathematics class at a small college. a) Explain why the class must have at least five male students or at least five female students. b) Explain why the class must have at least three male students or at least seven female students.

See explanation.

Step-by-step explanation:

There are nine students in a discrete mathematics class.

a) As there are two categories i.e male and female, so there would be at least

= 5  representative of one gender.

b) If class has less than 3 male students, then we know there are more than 9-3=6 female students.

Same goes for the other way that it class has less than 7 female students then we know there are more than 9-7=2 male students

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)