Math for Computer science
Questions 1 to 10
¬[pv (¬ pvq)] is logically equalent to
(a) pÙq (b)
¬ p Å ¬q (c) ¬
p Ù¬q (d) ¬
p Ù q (e) p
Ù ¬ q.


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)


A ÇÆ = Æ, is known as
(a) Indentity law (b)
Domination laws (c) Idempotent laws
(d) Absorption laws (e)
Complement laws.


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.


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.


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}.


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.


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.


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.


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.

Answer : (d)
Reason: {x
/ x is the square of an integer less than 100}
= {
1^{2}, 2^{2}, 3^{2}, 4^{2}, 5^{2}, 6^{2},
7^{2}, 8^{2}, 9^{2})
= {1,
4, 9, 16, 25, 36, 49, 64, 81}.


Answer : (b)
Reason: by
definition


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}.


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.


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}.


Answer : (c)
Reason: by
definition
A
B = {x / x ÎA and x Ï B}.


Answer : (b)
Reason: By
definition of preimage.


Answer : (c)
Reason: By
definition of surjection, for each b ÎB _{=}aÎ A ' f(a) = b.


Answer : (a)
Reason: By
definition.

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