MCA Assignments : CS-07 TMA Discrete Mathematics

MCA CS-07 TMA Discrete Mathematics

Course Code : CS-07
Course Title : Discrete Mathematics
Assignment Number : MCA(4)-07/TMA/04
Maximum Marks : 10
Last Date of Submission : 15th October, 2004

This is a Tutor Marked Assignment. There are four questions in this assignment. Answer all questions. You may use illustrations and diagrams to enhance explanations.

Question 1: Prove that in a complemented distributive lattice [L, V, ^ ], the a of an element a of L is unique.

(2 marks)

Question 2: Obtain the equivalent Principle Conjunctive Normal form of the formula:
( p ⇔ θ ) v ? R,

where ⇔, v and ?denote respectively bi-conditional, disjunction and negation operators.

(3 marks)

Question 3: A graph G has the following adjacency matrix A(G). Check whether it is connected or not.

Discrete Mathematics
(3 marks)

Question 4: Let A= R ~ {3} and B = R ~ {1} and a function f : A ? B is defined
as f (x) = x – 2 for x ? A.
x -3

Find
(i) whether f is 1 – 1
(ii) whether f is onto
(iii) f -1 , if it exists , else tell reason (s) why f 1 does not exist

(2 marks)

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