Sets P, Q, and R consist of the positive factors of 48, 90, and 56, respectively. If set T = P U (Q ∩ R), which of the following does NOT belong to T?

All students have to take at least one math class and one language class. Twenty students take calculus, and thirty students take statistics. Fifteen students take Spanish and twenty-five take French. If there are thirty-five students total, what is the maximum number of students taking both two math classes and two language classes.

The universal set is positive counting numbers less than 11. Set A = {1, 3, 5} and Set B = { 2, 4, 6}.

What is ?

The class of 2034 at Make Believe High School graduated 50 students. 13 students studied only math. 35 students studied English. 30 students studied only 2 subjects. Only 4 students studied writing, it was the third subject for all of them. How many students did not study anything?

In a class of senior high-school students, have pet cats, have pet dogs, have both cats and dogs, and have neither cats nor dogs. How many total students are in the class?

A group of high school juniors are taking Biology, Calculus, and Spanish as shown above. Which student is not in the set ?

Given the Venn diagram below, which of the following does not belong to ?

Giving the Venn diagram above, what is the sum of the numbers in the set ?

In a school of 1250 students, 50% of the students take an art class and 50% of the students take a gym class. If 450 students take neither art nor gym class, then how many students take both art and gym?

Forty students play soccer and/or basketball after school. Twenty-four students play soccer and twenty-nine play basketball. How many students play both soccer and basketball?