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.

Answers
51.

Answer : (a)
Reason: Three
letters without repetitions should be filled up in three places. So
L_{1} L_{2} L_{3}
26 25 24
Three digits can be filled
in three places can be filled with out repetitions are 10.9.8 ways.
D_{1} D_{2} D_{3}
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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