# Math for Computer science Questions and Answers 161 to 170

## Math for Computer science

### Questions 161 to 170

161.
Which of the following statement is false?
 (a) p Ú q           is equivalent to  not ((not p) Ù (not q)) (b) p Ú (not q)  is equivalent to  q → p (c) p →  q         is equivalent to  q → p (d) p → q         is equivalent to  (not q) → (not p) (e) p Ú q           is equivalent to  q Ú p.
162.
Denote (p Ù (not q) Ù (not r)) by f. Choose the correct statement from the following:
 (a) f is true when, p is true, q is true, r is true (b) f is true when, p is true, q is true, r is false (c) f is true when, p is false, q is false, r is true (d) f is true when, p is true, q is false, r is true (e) f is true when, p is true, q is false, r is false.
163.
Let R be the relation on {1, 2, 3, 4} defined by “x is less than y”. R is
 (a) {(1, 1), (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)} (b) {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)} (c) {(1, 1), (2, 2), (3, 3), (4, 4)} (d) {(2, 1), (3, 1), (4, 1), (3, 2), (4, 2), (4, 3)} (e) {{1, 2}, {1, 3},{1, 4}, {2, 3}, {2, 4}, {3, 4}}.
164.
Let R be a relation from the set A to set B. Which of the following is correct?
 (a) The domain of R is always equals to A (b) The domain of R is a proper subset of A (c) The domain of R is a proper subset of A consisting of the second elements of the ordered pairs of R (d) The domain of R is a proper subset of A consisting of the first elements of the ordered pairs of R (e) The domain of R is a subset of B.
165.
The symbols of vocabulary which cannot be replaced by other symbols are called
 (a) Terminals (b) Non-Terminals (c) Sentence (d) Productions (e) Word.
166.
The two Finite State Automata are called equivalent if they recognize
 (a) Same Grammar (b) Same Vocabulary (c) Same String (d) Same Language (e) Same Productions.
167.
An algorithm in which it solves a problem by reducing it to an instance of the same problem with smaller inputs.
 (a) Transitive (b) Procedure (c) Recursive (d) Input Output (e) Iteration.
168.
The value of f(3) given f(0) = f(1) = 1 and f(n + 1) = f(n) – f(n – 1) is
 (a) 1 (b) 2 (c) 0 (d) –1 (e) –2.
169.
If 7 ≡ 2 (Mod 5) and 11≡ 1(Mod 5), then
 (a) 77 ≡ 5 (Mod 5) (b) 77 ≡ 2 (Mod 5) (c) 77 ≡ 0 (Mod 5) (d) 77 ≡ 1 (Mod 5) (e) 77 ≡ 3 (Mod 5).

 170 Suppose that A is a subset if V*. Then the set consisting of concatenations of arbitrarily many strings from A represented by A* is called (a)  Symmetric closure                           (b)  Reflexive closure                   (c)  Kleene closure (d)  Finite closure                                   (e)  Finite state closure.