In a class of 40 students; 30 have taken science; 20 have taken mathematics
and 8 has neither taken mathematic nor science. Find how many students
have taken:
i)  both subjects.
ii) exactly one subject  

How many ways are there to distribute 15 district objects into 5 distinct 
boxes with: 
i)  At least three empty box. 
ii) No empty box. 

Show using truth  table that:
 (p→ q )→q ⇒   p ∨ q

How many words can be formed using letter of  UNIVERSITY  using each 
letter at most once? 
i)  If each letter must be used, 
ii) If some or all the letters may be omitted. 

There are two mutually exclusive events A and B with P(A) =0.7 and P(B) = 
0.6. Find the probability of followings: 
i) A and B both occur 
ii) Both A and B does not occur 
iii) Either A or B does not occur 

How many  different committees can be formed of 12 professionals, each 
containing at least 2 Professors, at least 3 Lecturers and 3 Administrative 
Officers, from a set of 5 Professors, 8 Lectures, and 5 Administrative 
Officers

Write the following statements in the symbolic form. 
i)  Some students can pass in exam. 
ii) Everything is having life.

Write down suitable mathematical statement that canbe represented by the 
following symbolic properties. 
i)  ( $ x) ( "y) ( "z) P 
ii) ( "x) ( " y) ( $ z) P