# Math for Computer science Questions and Answers 21 to 30

## Math for Computer science

### Questions 21 to 30

 21 A sentence is made up of (a)   Noun phrase proceeded by a verb phrase (b)   Noun phrase followed by verb phrase (c)   Noun phrase followed by Noun phrase (d)   Verb phrase followed by Noun phrase (e)   Verb phrase followed by a verb phrase. 22 Let a set A has a4 elements then P(A) denotes the powerset of the set A. Now cardinality of P(A) is (a) 16                      (b) 81                      (c) 256                    (d) 1                        (e) 4. 23 A function from set A to set B is one - to -one and onto, then the ferniction is known as (a) Sujection                                          (b) Injection                                           (c) Bijection (d) Homomorphism                                (e) Automorphism. 24 (pÙØq)®p is a (a) Contingency             (b) Contradiction           (c) Tautology     (d) Contrapositive          (e) Inverse. 25 The fallacy of denying the antecedent is denoted by (a) [(p®q)Ù p] ®q         (b) [(p®q)Ù Øp] ®Øq (c) [(p®q)Ù q] ®p         (d) (p®q)Ù Øq] ® Øp    (e) [(p®q)Ù Ør] ® Øq. 26 For which of the following ‘2’ is an element. (a) {2, {2}}              (b) {{2}, {{2}}} (c) {{2}, {{2, {2}} (d) {f, {2}}              (e) {{2}}. 27 Let F(x) : x is a pearl, P(x) : x is soft. The statement “All pearls are soft” equivalent (a) "x[F(x) Ù P(x)]          (b) "x[F(x) Ú P(x)]         (c) "x[F(x) « P(x)] (d) "x[F(x) ® P(x)]                    (e) "x[F(x), P(x)]. 28 Suppose that U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The bit string for the set A = {1, 3, 6, 10} is (a) 00 1110 0111            (b) 10 1001 0101            (c) 11 0110 0111 (d) 10 1001 0001            (e) 00 1010 1010. 29 Suppose that U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. The element of the set for which the bit string is 11 1100 1111 (a) {0, 1, 2, 3, 5, 7, 8, 9, 10}        (b) {1, 2, 3, 4, 7, 8, 9, 10}           (c) {1, 3, 5, 6, 7, 8, 9, 10}            (d) {2, 3, 4, 7, 8, 9, 10} (e) {1, 3, 4, 5, 6, 7, 8, 9, 10}. 30 Find the value of éë1/2û + é1/2ù + 1/2ù (a) 1 (b) 2 (c) 0 (d) 0.5     (e) 1.5.

21.
Reason:  By definition of the sentence.
22.
Reason:  n(A) = |A| = 4 = cordinality of A
|P(A)| = cardinality of power set of A
= 24
= 16.
23.
Reason:  By definition of bijection.
24.
Reason:
 P Q ùQ P Lù Q (P Lù Q) ®P F F T F T F T F F T T F T T T T T F F T
\ (PLùq) ® P is a Toutology.
25.
Reason:  by definition
26.
Reason:  by definition
27.
Reason:  for all x
If x is a pearl then x is soft
\ "x, [f(x) ® P(x)]
28.
Reason:  Bit string of A = {1,3,6,10} in U = {1,2,3,4,5,6,7,8,9,10} is 1010010001
29.
Reason:  U = {1,2,3,4,5,6,7,8,9,10} the elements for which bit string is 1111001111 is {1,2,3,4, 7,8,9,10}
30.