| Course Code |
CS-07
|
| Course Title |
MCA-(4)ICS-07/TMA/2003 |
| Assignment Number |
Discrete
Mathematics |
| Maximum Marks |
10 |
| Last Date of
Submission
|
15th October,
2003 |
This is a Tutor Marked Assignment. There are two questions in
this assignment. Answer all the questions. You may use illustrations
and diagrams to enhance explanations. Please go through the
guidelines regarding assignments.
| Question 1: |
|
Design the
following circuits, clearly explaining the steps involved:
(a) A majority function is generated in a circuit when the
output is equal to 1, if the output variables have
more
1's than 0's. The output is 0
otherwise. Design a three-input majority function using only NAND
gates.
(b) Design a circuit that accepts a three-bit number
and generates an output binary number equal to
the
square of the input number.
|
| Question 2: |
(a) |
Prove that
in a complemented and distributive lattice [L, È
, Ç ],
the complement a' of an element
a of L is unique. |
| |
(b) |
If we define
a tree as a finite, undirected graph with no cycles, then
prove that a graph with n vertices is a tree if and only if it is
connected and has exactly (n - 1) edges. |
| Question 3. |
|
Translate the
following English arguments into Propositional Calculus (PC) and
decide, in PC, for each argument, whether it is a valid argument or
not:
Argument (i) Given the statements
(a) If predestination is true, then God
causes us to sin.
(b) If God causes us to
sin and yet damns sinners to eternal punishment, then God is
not good.
Therefore,
we conclude:
(c) If God is good,
their either predestination is not true or else God does not
damn sinness to eternal punishment.
Argument (ii) Given the statements
(a) If determinism
is true then we have no free will.
(b) If Heisenberg's interpretation of
quantum physics is correct, then there are events not
casually
necessitated
by prior events.
(c) If there are events
not casually necessitated by prior events, then we have free
will.
Therefore, we conclude:
If Heisenberg's
interpretation of physics is correct, then we have free will.
| |