(b) 3
(c) 3
(d) 83
2. (a) λ
(b) aababab
(c) babababa
3. (a) Function is defined for all natural numbers divisible by 9.
(b) Function is defined for all x ≥ 5
(c) Function is defined for all N.
(d) Function is defined for all N.
13. A (2, 4) = 11; A (3, 3) = 37.
CHAPTER 8
1. (a) Yes, T
(b) No
(c) No
(d) Yes, F
(e) Yes, T
(f) Yes, F
(g) Yes, T
2. (a) Summer in Kodaikanal is not hot or it is not Sunny
(b) There is air pollution in Karuppur.
(c) 7 8 15
+ ≠
(d) Today is not friday.
3. (a) ¬ p
(b) p q
→
(c) p q
→
(d) q
p
→
5. (a) True
(b) True
(c) True
7. (a) If your guarantee is good, then you must have bought your PC less
than 1 year ago.
(b) If you drive more than 800 kilometers, then you have to buy diesel.
8. (a) Converse: A positive integer is a prime if it has no divisors other
than 1 and itself.
Contrapositive: If a positive integer has a divisor other than 1 and
itself, then it is not prime.
(b) Converse: If I goto class there will be a test.
Contrapositive: If I do not go to class, then there will not be a test.
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Theory of Automata, Formal Languages and Computation