DISCRETE STRUCTURE
SEM-III, 2012-13
B.TECH EXAMINATION
UTTARAKHAND TECHNICAL UNIVERSITY
(UTU)
Time: 3 Hours
Total
Marks: 100
Do any four Questions:
- Draw Venn Diagram for (A ∩ B) ⋃ C.
- If f: R→R is a function such that f(x) = 3x + 5
prove that f is one - one onto. Also find the inverse of f.
- Determine the number of integer solutions to the
equation:
x1 + x2 + x3 + x4 = 7
where xi > =0 for all i = 1,2,3,4 - Confirm or disprove the following identities:
(A ⋃ B) X (C ⋃ D) = (A X C) ⋃ (B X D) - Let {A1, A2 ...Ak} be
a partition of set A. We define a binary relation R on A such that an
ordered pair (a, b) is in R if and only if a and b are in the same block
of the partition. Show that R is an equivalence relation.
- Show that among n+1 positive integers less than or equal to 2n there are two of them that are relative prime.
