# Math for Computer science Questions and Answers 61 to 70

## Math for Computer science

### Questions 61 to 70

 61 Which one of the following statements is false? (a)                           ∅x A = ∅                                               (b) AXB = BXA (c)                           R–1 = {(y, x), (x, y) ∈R}                            (d) Domain of R-1= Range of R. (e)                           A relation on A is a subset of AXA. 62 List the ordered pairs in the relation R from A={0,1,2,3,4} and B={0,1,2,3} where (a,b) ∈ R iff lcm(a,b) = 2. (a)                           {(1,2), (2,1),(2,2)}      (b) {(1,2), (2,1)} (c)                           {(1,2), (2,1),(2,4)}      (d) {(1,2), (2,1),(2,2),(2,4)} (e)                           {(2,1),(2,2),(2,4)}. 63 Which one of the following properties is not satisfied by the divides relation on the set of integers? (a) Reflexive                                          (b) Not symmetric (c) Not antisymmetric                             (d) Transitive           (e) Antisymmetric. 64 Which one of the collection of sets given below is the partition of the set Z×Z ? (a)   The set of pairs (x,y) where x or y is odd; The set of pairs (x,y) where y is even. (b)   The set of pairs (x,y) where x and y are odd; The set of pairs (x,y) where exactly one of x and y is odd; The set of pairs (x,y) where x and y are even. (c)   The set of pairs (x,y) where x is positive; The set of pairs (x,y) where y is positive; The set of pairs (x,y) where both x and y are positive. (d)   The set of pairs (x,y) where x ≠ 0 and y≠ 0; The set of pairs (x,y) where x=0 and y≠ 0; The set of pairs (x,y) where x ≠ 0 and y= 0. (e)   None of the above. 65 A function f(x) = x+1/x–1 will not be defined for x = ________. (a) 0                        (b) 1                        (c) ½                       (d) 2                        (e) –1. 66 The domain and range of the function that assigns to each non-negative integer its last digit are (a)                           0-Z, Z                      (b) Z, Z+                 (c) Z+,Z+                 (d) Z+,{0..9}                              (e)                           Z+,Z. 67 According to RSA encryption algorithm the encryption key consists of modulus n = pq where p and q are large primes and exponent e. Here e is relatively prime to ­_________. (a)                           pq where p,q are large prime numbers (b)                          p(q-1) where p,q are large prime numbers (c)                           (p-1)q where p,q are large prime numbers (d)                          (p-1)(q-1) where p,q are large prime numbers (e)                           (p+1)(q+1) where p,q are large prime numbers. 68 A composite integer n that satisfies the congruence ­­­­­­­­­­­­­­­__________ for all positive integers b with gcd(b,n) = 1 is called a Carmichael number. (a) bn–1 ≡ 1 (mod n)                                 (b) bn ≡ 1 (mod n) (c) bn–1 ≡ b(mod n)                                  (d) bn+1 ≡ 1 (mod n) (e) bn–1 ≡ 1 (mod n+1). 69 a= (1110)2 and b= (1011)2, a+b = ? (a) 1111                   (b) 10001                 (c) 11001                 (d) 10011                 (e) 10111. 70 If a student has to select one project from three lists, first containing 23 projects second containing 15 projects and third containing 19 projects, the total number ways to select the projects is (a)                           57                           (b) 6555                  (c) 6554                   (d) 56   (e) 58.