Math Assignment for BCA 2nd Sem.

R.C.INSTITUTE OF TECHNOLOGY

(AFFILIATED TO G.G.S.I.P.UNIVERSITY)

ASSIGNMENT: MATHEMATICS-II (BCA-102)                                               DATE:2013

PURPOSE: This assignment covers questions from UNIT I and UNIT II. It will help students understand the concepts of

·         SETS ,RELATION AND FUNCTIONS

·         PARTIAL ORDER SETS AND LATTICES

Questions:

Q.1) State and prove De-Morgan’s law in sets

Q.2) Define reflexive, symmetric and transitive relations in terms of graphs

Q.3)Define recursive, congruence modulo and hashing functions.

Q.4) For each of the following poset; draw the Hasse diagram and determine all maximal and minimal elements and greatest and least elementsif they exist. specify which posets are lattices.

a) [D₂₀;|]

b) [D_30;|]

c)[A,|]; where A={2,3,4,6,8,24,48}

Q.5)  Using arithmetic modulo M=15, evaluate

i) 9+13           ii) 7+11          iii) 4-9                        iv) 2-10

Use a+MΞ a (mod M)

Q.6) Given A= {1, 2, 3} and B={x, y, z}. Let R be the relation from A to B defined as    R={(1,x), (3,x),(3,y), (3,z)}

i) Determine the matrix of relation R

ii) Find the inverse relation R^-1 of R and determine its matrix

iii) Determine the domain and Range of R                                                     

 

SHWETA SINHA

(ASSIST. PROFESSOR)