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

a)There are genders,males and females,so at least(9/2=5) representatives of each gender.

b) If the less than 3 male students then there are more than 6 female students and if the class has less than seven female students than there are more than 2 male students.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.