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.

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.


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.


(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.

Answers
21.

Answer : (b)
Reason: By
definition of the sentence.


Answer : (a)
Reason: n(A)
= A = 4 = cordinality of A
P(A)
= cardinality of power set of A
=
2^{4}
=
16.


Answer : (c)
Reason: By
definition of bijection.


Answer : (c)
Reason:
\ (PLùq) ® P is a Toutology.


25.

Answer : (b)
Reason: by
definition


26.

Answer : (a)
Reason: by
definition


27.

Answer : (d)
Reason: for
all x
If x is a pearl then x is soft
\ "x, [f(x) ® P(x)]


28.

Answer : (d)
Reason: Bit
string of A = {1,3,6,10} in U = {1,2,3,4,5,6,7,8,9,10} is 1010010001


29.

Answer : (b)
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.

Answer : (b)
Reason: éë1/2û + é1/2ù +1/2ù = éë0.5û + é0.5ù +1/2ù
= é0 + 1 +1/2ù
= é3/2ù = é1.5ù = 2

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