Set F_{n} gives all factors of n. Set M_{n} gives all multiples of n less than 1000. Which of the following statements is/are true?
i. F_{108} ∩ F_{84 }= F_{12}
ii. M_{12} ∪ M_{18} = M_{36}
iii.M_{12} ∩ M_{18} = M_{36}
iv.M_{12} ⊂ M_{6} ∩ M_{4}
A´ is defined as the complement of A, as in, set of all elements that are part of the universal set but not in A. How many of the following have to be true?
i. {n(A ∪ B)' =n(A' ∩ B')}
ii. If {A ∩ B=0}, then {A' ∪ B'} is equal to the universal set
iii. If {A ∪ B} = universal set, then {A' ∩ B'} should be the null set.
iv. If {A ⊂ B} then {A' ∪ B'=(A ∩ B)'}
Of 60 students in a class, anyone who has chosen to study maths elects to do physics as well. But no one does maths and chemistry, 16 do physics and chemistry. All the students do at least one of the three subjects and the number of people who do exactly one of the three is more than the number who do more than one of the three. What are the maximum and minimum number of people who could have done Chemistry only?
John was born on Feb 29^{th} of 2012 which happened to be a Wednesday. If he lives to be 101 years old, how many birthdays would he celebrate on a Wednesday?
How many of the following statements have to be true?
i. No year can have 5 Sundays in the month of May and 5 Thursdays in the month of June.
ii. If Feb 14^{th} of a certain year is a Friday, May 14^{th} of the same year cannot be a Thursday
iii. If a year has 53 Sundays, it can have 5 Mondays in the month of May.