MCS013: Discrete Mathematics
Year: 2005 TEE: December Time 2 Full Marks 50
Note: Question 1 is compulsory. Answer any three from the rest.
Q.1(a): Wrtie the negation of the following statements:
(i) For all x, x2 < x.
(ii) There exists x such that x2 = 2.
| Q.1(b): Construct the cicuit that produces the follwoing output:
x'/ (y / z')': [4]
Q.1(c): Let A = {1,2,3,4,5}. Construct a relation R from A to A such that R is reflexive and symmetric but not transitive': [4]
Q.1(d): Prove by induction that n3 - n is divisable by 3 for all positive integers.: [4]
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