# Math for Computer science Questions and Answers 51 to 60

## Math for Computer science

### Questions 51 to 60

51.
How many different license plates are available if each plate contains a sequence of three letters followed by three digits when repetitions are not allowed?
(a) 26.25.24.10.9.8                                 (b) 26.26.26.10.10.10 (c) 26C3, 10P3
(d) 26C3, 10C3                                       (e) 26!, 10!.
52.
Which of the following is true for a relation R : A ®B, a Î A, b Î B?
(a)   A relation R is Reflexive if aRb
(b)   A relation is symmetric if aRb Þ bRa
(c)   A relation is Transitive if aRb, aRc Þ aRb
(d)   A relation is anti symmetric if aRb, bRc Þ a =c
(e)   A relation is anti symmetric if aRb, bRa Þ a ¹b.
53.
The propositions p and q are logically equivalent if
(a)                           p→q is a tautology  (b) q→p is a tautology
(c)                           p↔q is a tautology  (d) ¬p↔¬q is a tautology
(e)                           ¬q↔¬p is a tautology.
54.
Identify the missing values from the below truth table.
 P Q (P ÅQ) F F F T T F T T T F
(a) T,T          (b) T, F  (c) F,F                         (d) F, T            (e) cannot be determined.
55.
What is the correct sequence of logical operators?
(a) ¬, ∧, ∨, → , ↔                                 (b) ¬, ∨,∧, → , ↔ (c) →, ↔, ∧,∨, ¬
(d) ∧, ∨, → , ↔,¬                                  (e) ¬, ∧, ∨, ↔, →.
56.
For any proposition ,the idempotent law states that
(a) pÚp º p              (b) pÙp º p              (c) pÙT º p              (d) a & b                 (e) b & c.
Let P be the proposition "It is snowing",
Q be the proposition "I will go the beach", and
R be the proposition "I have time".

Which of the following is the logical equivalent of the English sentence
"If it is not snowing and I have time, then I will go to the beach",

(a) (P∧ Q) → R                                      (b) (P∨ Q) → R        (c) (¬P∧ R) → Q
(d) (¬P∨ Q) → R                                    (e) (¬P∨ Q) ↔ R.
57.
Let p(x) be the statement “x ≥ x2”. If the universe of discourse consists of the integers which of the following propositions are true?
(a)                           P(0)                        (b) P(1)                                                  (c) ∃xp(x)
(d) All of the above  (e) None of the above.
58.
Kangaroos live in Australia and are marsupials. Therefore kangaroo is a marsupial.
Which rule of inference is used in the above argument?

(a) Addition             (b) Simplification                                   (c) Modus ponens
(d) Modus tollens    (e) Resolution.
59.
The set A= {a,b} P(A) = ?
(a) {∅,{a},{b},{a,b}}                                  (b) {{a},{b},{a,b}}
(c) {∅,{a},{b}}                                          (d) {{∅},{a},{b}}         (e) {{∅},{a},{b},{a,b}}.
60.
In a group of 20 people 18 like pink color and 7 like green color. How many people like both the colors?
(a) 3                                                      (b) 4                        (c) 5                        (d) 7    (e) 11.

Answers

 51 Answer :           (a) Reason:            Three letters without repetitions should be filled up in three places. So           L1         L2         L3           26         25         24           Three digits can be filled in three places can be filled with out repetitions are 10.9.8 ways. D1      D2         D3         10      9          8 So three letters followed by three digits can be filled in 26.25.24.10.9.8 ways 52 Answer :           (b) Reason:  By definition. 53 Answer :           (c) Reason :           The propositions p and q are logically equivalent if p↔q is a tautology. That means p↔q is always true. 54 Answer :           (d) Reason :           XOR is true if both the propositions are either true or false. 55 Answer :           (a) Reason :           The given sequence is the correct sequence of logical connectives. 56 Answer :           (d) Reason :           the idempotent laws are . pÚp º p; pÙp º p. 57 Answer :           (c) Reason :           the logical equivalent of the English sentence                         "If it is not snowing and I have time, then I will go to the beach", is c. (¬P∧ R) →Q 58 Answer :           (d) Reason :           The statement is “x≥x2”. P (0) is true since 0 ≥ 02 ; P(1) is true since 1 ≥ 12 . ∃xp(x) is also true because we can find atleast one example for which x≥x2 .So the options a b and c are true. Thus the answer d. 59 Answer :           (b) Reason :           Let p be Kangaroos live in Australia Let q be Kangaroos are marsupials. The rule of inference (p Ù q) → q is simplification. 60 Answer :           (a) Reason :           P(A) is the power set of A which is {,{a},{b},{a,b}}

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