Given: U = {Even numbers between 0 and 30} P = {Multiples of 6 between 0 and 30} Q = {Multiples of 4 between 0 and 30} Find (P∪Q)c

Answer Details

In set theory, the complement of a set A, denoted by A', is the set of all elements in the universal set that are not in A. In this question, we are given three sets: U, P, and Q. U is the set of even numbers between 0 and 30, P is the set of multiples of 6 between 0 and 30, and Q is the set of multiples of 4 between 0 and 30. To find (P∪Q)c, we first need to find P∪Q, which is the union of P and Q. The union of two sets is the set of all elements that are in either set. In this case, P∪Q is the set of all multiples of either 4 or 6 between 0 and 30. We can list out the elements of P∪Q: {0, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30} To find (P∪Q)c, we need to find the complement of P∪Q, which is the set of all even numbers between 0 and 30 that are not multiples of either 4 or 6. We can list out the even numbers between 0 and 30 that are not multiples of 4 or 6: {2, 10, 14, 22, 26} Therefore, the answer is option A: {2, 10, 14, 22, 26}.