**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, x^{2} < x. (ii) There exists x such that x^{2} = 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 n^{3} - n is divisable by 3 for all positive integers.: [4]
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