Set Theory

Challenge Yourself: Practice Problems to Solidify Concepts of Set Theory

  1. Out of the 30 students of a class 20 like football and 15 like cricket. The number of students who like both the games is 10. Determine using a Venn diagram the number of students who do not like either of the games.
  2. Out of 100 students 65 passed in Bangla, 48 in both Bangla and English and 15 failed in both the subjects.
    1. Express the above in a Venn diagram along with a brief description.
    2. Determine the number of students who passed only in Bangla or passed only in English.
    3. Determine union of the sets of prime factors of the number of students passed and failed in both the subjects.
  3. Given that A = {x,y}, B = {x,y,z} and C = (A U B), show that the number of elements of P(C) is 2n , where n is the number of elements of C.