Mathematics 2005 JAMB Past Questions - Question 10: If U={x/x is a positive integer less than 10} and P={x/x is a prime factor of 30},find the complement of P.

Correct Answer

C

Explanation

To find the complement of set P, we need to determine the elements that are not in P but are in the universal set U.First, let's determine the prime factors of 30. The prime factors of 30 are 2, 3, and 5.Therefore, the set P = {2, 3, 5}.To find the complement of P, we need to identify the elements in U that are not in P.The universal set U consists of positive integers less than 10: U = {1, 2, 3, 4, 5, 6, 7, 8, 9}.The complement of P, denoted as P', will contain the elements of U that are not in P.P' = U - PP' = {1, 4, 6, 7, 8, 9} - {2, 3, 5}P' = {1, 4, 6, 7, 8, 9}Therefore, the complement of P is {1, 4, 6, 7, 8, 9}.