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August 2011 BachelorofScience inInformationTechnology(BScIT) Semester2/ Diploma inInformationTechnology(DIT) Semester2 BT0069DiscreteMathematics4CreditsAssignmentSet 1 (60 Marks)Answer allquestions 6 x 10=60 Marks (Book ID: B0953)

2 1 1 ( 1. If f: R R is defined by f x ) = x 3x + 5 find (i) f ( 3) and (ii) f ( 15)

A , ,I 2. 3 URYH WKDW1 A2 .....,An are subsets of S. Then the non-empty minsets , generated by A1,A2 .....,An IRUP D SDUWLWLRQ RI 6. ,n 3. Solve an 2an1 =( n + 1)2

4. In a finite Poset S, show that there is always atleast one maximal element and one minimal element. _. 6KRZ WKDW ,I / LV D GLVWULEXWLYH ODWWLFH, WKHQ LW LV D PRGXODU ODWWLFH. 6. Show that the set of real numbers is a group with respect to multiplication.

August 2011 BachelorofScience inInformationTechnology(BScIT) Semester2/ Diploma inInformationTechnology(DIT) Semester2 BT0069DiscreteMathematics4CreditsAssignmentSet 2 (60 Marks)Answer allquestions (Book ID: B0953)

1. Show that((

p ~q ) r ) p q r )) ( (( xP x )) ( ( xQ x )) (

6 x 10=60 Marks

( ( ( 2. Show that x P x ) Q x ))

3. Consider the Boolean expression

f( x1, x2, x3 ) = x1 ( x2dnf and cnf.

[

x3 )

] [( x

1

x 2 ) x3

]

x1 over({

]

,0},1 , , ). Write

S S 4. If G =({ S }, { ,0},1 {: 0S ,1 }, S ), then find L(G), the languagegenerated by G. _. 3URYH WKDW ,Q D JUDSK *, HYHU\ X-v path contains a simple u-Y SDWK _. 3URYH WKDW ,I D ELQDU\ Q-tuple (x , x),is transmitted across a binary 1 2 n ..,[ symmetric channel with probability p such that no error will occur in each coordinate,

n k nk then the probability that there are errors in exactly k coordinates is q p . k