If a, b, c are in A.P. show that  are also in A.P.

400 patients in a hospital were investigated for kidney and lung disorders. It was found that 240 of them had kidney disorder, 80 had lung disorder and 40 of them had both. Find the number of patients who had.

(a) at least one of the two disorders.

(b) kidney disorder but not the lung disorder

(c) lung disorder but not the kidney disorder

(d) neither of the two disorders.

In a group of students, 100 students know Hindi, 50 know English and 25 know both the languages. Find the number of students in the group if

(a) each student knows at least one of the two languages.

(b) 15 students in the group do not know any of the two languages.

A, B, C are three sets such that :n(A ∪ B ∪ C)= 100.

n (A) = 40, n (B) = 47, n (C) = 51, n(A ∩ B) = 13,n(B ∩ C)= 17,n(C ∩ A)= 16. Find n(A ∩ B ∩ C).

In a group of 50 people, 30 like to play cricket, 25 like to play football and 32 like to play hockey. Assume that each person in the group likes to play at least one of the three games. If 15 people like to play both cricket and football, 11 like to play football and hockey and 18 like to play cricket and hockey. Find :

(a) How many like to play all three games?

(b) How many like to play only football?

(c) How many like to play only hockey?

(d) How many like to play exactly one game?

If  show that area of

   sq. units.

Let A = collection of all the vowels of the alphabet. Insert appropriate symbol ∊ or ∉ in the blank spaces. 

(i) v .............. A         (ii)   u ............. B                  (iii)   a .............. A