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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

+= =