Math for Computer science
Questions 231 to 240
231.

A drawer contains 4 red pens, 5 blue
pens and 2 black pens. If you reach into the drawer without looking and pull
out a pen for you and a pen for your work partner to own them, what is the
probability that the first pen will be blue and the second pen will be black?


You and 5 friends go on a roller
coaster in which each car holds a pair. How many different pairs can you and
your friends create for the ride?


A pair of dice is thrown. What is
the probability of both the faces not
having the same number throwing a double?


You and a group of 9 friends are
playing basketball in a local park. At the end of the game, if each player
shakes hands with every other player, how many handshakes will there be?


A simple theorem used in the proofs
of the other theorems


Let A = {1, 2, 3}, B = {2, 3, 4} and
U = {1, 2, 3, 4, 5, 6, 7}. What is the value of _{}


If two sets A and B, A is a subset
of B and A ≠ B then A is called
–––––––––– of B.


The inductive step for strong
induction is


Which of the following relations is
antisymmetric on the set of positive integers?


If f: z→z is defined by f(x) = 1 if
x is even, f(x) = –1 if x is odd, f(x)
= 1, if x = 0, then f is a mapping. What is the codomain and range of f
respectively.

Answers
231.

Answer : (e)
Reason: drawing a blue pen is 5/11 drawing a black pen is after not
replacing the blue pen is 2/10 drawing both is 5/11*2/10=1/11

Answer : (c)
Reason: total there are 6 people including you
so the total number of ways pairs can be formed is gieven by ^{6}C_{2} = 15


Answer : (b)
Reason: The probability of throwing a diouble is
6/36.
The
probability of not throwing a diouble
is 1 6/36 = 30/36 = 5/6


Answer : (c)
Reason: along with you there are 10 people, out of tehm hand shaking must
be done, so two people shakes the hands. total number of ways hand shaking
takes place is given by ^{10}C_{2} = 45 ways.


Answer : (c)
Reason: by definition of lemma


Answer : (a)
Reason: B^{c} = {1,5,6,7 }
A^{c
}_{ }= { 4,5,6,7 }
B
 A^{c } =
{ 2,3,}
B^{c
}– (BA^{c}) = {1,5,6,7 }


Answer : (c)
Reason: by the definition of proper subset


Answer : (b)
Reason: by the definition of strong induction


Answer : (b)
Reason: by the definition of antisymmetric


Answer : (d)
Reason: as the function is defined on z to z so the codomain is z
(integers) and the only integers which
are mapped by the function are 1, 1 so the range is {1,1 }.

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