Math for Computer science Questions and Answers 1 to 10

Math for Computer science

Questions  1 to 10

1.	¬[pv (¬ pvq)] is logically equalent to (a) pÙq                   (b) ¬ p Å ¬q            (c) ¬ p Ù¬q             (d) ¬ p Ù q              (e) p Ù ¬ q.
2.	The member of the set {x / x is the square of an integer less than 100} (a) {1, 4, 9, 16, 25, 36, 49, 64}                 (b) {1, 4, 9, 16, 25, 36, 64, 81}                 (c) {1, 4, 9, 16, 36, 49, 64, 81}                 (d) {1, 4, 9, 16, 25, 36, 49, 64, 81}           (e)
3.	A ÇÆ = Æ, is known as (a) Indentity law                                      (b) Domination laws (c) Idempotent laws (d) Absorption laws                                (e) Complement laws.
4.	Let A = {0, 2, 4, 6, 8, 10}; B = {0, 1, 2, 3, 4, 5, 6} A È (B  A) is given by (a) {0, 2 4, 6, 8, 10}                                 (b) {0, 1, 2, 3, 4, 5, 6}                             (c) {0, 1, 2, 3, 4, 5, 6, 10}                        (d) {0,1, 2, 3, 4, 5, 6, 8}                           (e) {0, 1, 2, 3, 4, 5, 6, 8, 10.
5.	Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} then bit string for the set A = {1, 5, 7, 8, 9} is (a) 0 1 0 0 0 0 0 1 1 1 0                           (b) 0 1 0 0 0 1 0 1 1 1 0                          (c) 0 1 0 0 0 1 1 0 1 1 0                           (d) 0 1 0 0 0 1 0 1 0 1 0 (e) 0 1 0 0 0 1 0 1 1 0 1.
6.	Let U = {0, 1 2, 3, 4, 5, 6, , 8, 9, 10}. the set represented by the bit string 0 1 0 1 1 1 1 0 0 0 0 is (a) {0, 2,7 8, 9, 10}                                  (b) {1, 3, 4, 5, 6}       (c) {1, 3, 4, 6, 7} (d) {1, 3, 4, 5}                                         (e) {0, 1, 3, 4, 6}.
7.	The set {x / x Î A and x Ï B} is defined by (a) A complement                                  (b) B  A                                               (c) A - B                              (d) (AÇB)                                               (e) B complement.
8.	Let f is a function from A to B. for aÎ A such that f (a) = b then 'a' is called (a) image                                               (b) pre image           (c) range element     (d) codomain element                                                           (e) mapping.
9.	Let f be a function from A to B. 'f' is said to be a surjective function if (a) for each aÎ A bÎ B ' f (a) = b             (b) for each b ÎA $ aÎ B ' f (a) = b (c) for each aÎ B aÎ A ' f (a) = b              (d) for each bÎ Ba ÎA ' f (b) = a (e) for each a ÎB b ÎA ' f (b) = a.
10.	Let 'n' be a positive integer. Then which of the following are true for a real number 'x'. (a) x + n = x + n                                                         (b) x + n = x + n (c) x + n = x + n (d) x + n = x + n                                                         (e) x + n = x + n

Answers

1.	Answer : (c) Reason:  ¬ [(p Ú ¬p) Ù (p v q)] ¬(p Ú ¬p) v ¬ (p v q) ¬(T) v ¬ (p v q) F v ¬ (p v q) ¬ (p v q) ¬ p v ¬ q.
2.	Answer : (d) Reason:  {x / x is the square of an integer less than 100} =     { 12, 22, 32, 42, 52, 62, 72, 82, 92) =     {1, 4, 9, 16, 25, 36, 49, 64, 81}.
3.	Answer : (b) Reason:  by definition
4.	Answer : (e) Reason:  A = {0, 2, 4, 6, 8, 10}               B = {0, 1, 2, 3, 4, 5, 6}               B  A = {1, 3, 5}               A È (B  A) = {0, 1, 2, 3, 4, 5, 6, 8, 10}.
5.	Answer : (b) Reason:  U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}               A= {1, 5, 7, 8, 9}               bit string of set A is 01000101110.
6.	Answer : (b) Reason:  U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}               bit string of set A is 01011110000               A = {1, 3, 4, 5, 6}.
7.	Answer : (c) Reason:  by definition               A  B = {x / x ÎA and x Ï B}.
8.	Answer : (b) Reason:  By definition of preimage.
9.	Answer : (c) Reason:  By definition of surjection, for each b ÎB =aÎ A ' f(a) = b.
10.	Answer : (a) Reason:  By definition.