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FBCA-04April-2008
Advanced MathematicsTOTALMARKS: 70 TIME: 3 HOURS
Instructions: - There are five questions. Each question carries14 marks.
Q-1 (A) Attempt any three of the following.[9]
(1) There are 400 students in a mathematics class and
600 students in Biology. Find the number of studentwhich are either in mathematics class or biology classin the following cases:
(1) The two classes meet at the same hour.
(2) two classes meet at the different hours and 200 students are
enrolled in both the subjects.
(1) ( ) 0
( ) ( ) ( ) ( )
( ) 400 600 0
( ) 1000 (1)
(2) ( ) 200
( ) ( ) ( ) ( )
( ) 400 600 200
( ) 800 (2)
n A B
n A B n A n B n A B
n A B
n A B
n A B
n A B n A n B n A B
n A B
n A B
=
= +
= +
=
=
= +
= +
=
L L L L
L L L
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(2)Let A={x/xN}, B={x/x=2n,nN}, C={x/x=2n-1,nN},D={x/x is a prime number}
Find
(1) A I B (2) C I D
(2) D-A (4) B-C
(5) B I C (6) A I C A={1,2,3,4,., n}
B={2,3,4,5, n}
C={1,3,5,7,, n}D={1,3,5,7,., n}
(1) A I B={2,3,4,5,...,n}(2) C I D={1,3,5,7,., n}(3) D-A={2,4,6,, n}
(4) B-C={2,4,6,, n}
(5) B I C={3,5,7,.., n}
(6) A I C={1,3,5,7,., n}
(3) Shade the following sets in the Venn diagrams.
(1) A I (C-B) (2) B- (A I C)
(1) A I (C-B)
C-B =
(2) B- (A I C)
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A I C = B- (A I C) =
(4) Define:
(1)Disjoint sets:-
The sets are said to be disjoint set if none of the elements are common inboth the sets.
(2) Symmetric different sets: -
If A and B are any two sets, the set of elements that belongs to A or B but
not in both is called symmetric difference of A and B and is denoted by A B.
(3) Cartesian Product of sets: -If A and B are sets, the set of all ordered pairs whose first components
belongs to A and second components belong to B is called Cartesian product of A and Bis denoted by AB.
Q-1 (B) Define Any Two of the Following. [5]
(1) Write the set {2 3 4 100
, , ,.........,3 2 3 99
} in the Set Builder Form.
ANS:( )1
{ / , 100}X
A X X X X
+= =
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