Worksheets1-50 dis math
Total questions: 50
Worksheet time: 25mins
Let R ={(a, b), (b, c), (c, a)} and S = {(b, a), (b, c), (c, c), (d, a)} be relations on A = {a, b, c, d}.
Find Composite Relation: S o R.
{(b, b), (b, a), (c, a), (d, b)}
{(a, a), (a, c), (b, c)}
{(a, a), (b, b), (c, c), (d, a)}
{(a, a), (b, a), (c, a), (c, b), (d, b), (d, c)}
What are the equivalence classes of 0 for congruence modulo 10?
[0] = {..., -20,- 10, 0, 10, 20,...}.
[0] = {..., -25,-15, 0, 15, 25, ... }.
[0] = {...,- 11,- 10, 0, 10, 11, ... }.
[0] = {..., -5,-10, 0, 10, 20, ... }.
Determine whether the relations for the directed graphs shown in below figure are reflexive, symmetric, and/or transitive
it is reflexive, symmetric and transitive
it is not reflexive, symmetric, and transitive
it is reflexive, neither symmetric and not transitive
it is not reflexive, neither symmetric and transitive
One hundred tickets, numbered 1, 2, 3,..., 100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a
grand prize (a trip to Tahiti). How many ways are there to award the prizes if the person holding ticket 4 wins the grand prize?
87456
253258
86523
941094
Thirteen people on a softball team show up for a game. How many ways are there to choose 10 players?
P(3,13)
P(10,13)
130
C(10,13)
The English alphabet contains 21 consonants and 5 vowels. How many strings of four letters of the English alphabet contain exactly one consonant?
840
46305
2625
10500
A relation on a set A is called an equivalence relation if it is
reflexive, symmetric, and transitive
transitive, antysymmetric, and symmetric
reflexive, antysymmetric, and symmetric
reflexive, antysymmetric, and transitive
List the ordered pairs in the relation on {0, 1, 2, 3} corresponding to the matrix:
{(1, 3), (1, 4), (2, 1), (2, 2), (3, 1), (3, 3), (4, 1)}
{(0, 2), (0, 3), (1, 1), (1, 2), (2, 1), (2, 2), (3, 0)}
{(0, 1), (0, 2), (0, 3), (1, 1), (2, 0), (2, 2), (3, 0)}
{(0, 2), (0, 3), (1, 0), (1, 2), (2, 1), (2, 2),(3, 0)}
A drawer contains a dozen brown socks and a dozen black socks, all unmatched. A man takes socks out at random in the dark. How many socks must he take out to be sure that he has at least three black socks?
12
3
5
15
List the triples in the relation {(a, b, c) | a, b and c are positive integers with
R= {1 < a+b ≤ c≤ 4}
{(1, 2, 1), (0, 1, 3), (1, 1, 2), (2, 1, 1), (1, 0, 3), (3, 0, 1)}
{(1, 1, 2), (1, 1, 3), (1, 1, 4), (1, 2, 3), (1, 2, 4), (2, 1, 3), (2, 1, 4), (1, 3, 4), (3, 1, 4)}
{(0, 1, 2), (0,1, 3), (0, 1, 4), (0, 2, 3), (0, 2, 4), (1, 0, 2), (1, 0, 3), (1, 0, 4), (2, 0, 3), (2, 0, 4)}
{(0, 2, 3), (0, 2, 4), (2, 0, 3), (2, 0, 4), (1, 1, 3), (1, 1, 4), (0, 3, 4), (3, 0, 4)}
A bowl contains 8 red balls and 8 green balls. A woman selects balls at random without looking at them. How many balls must she select to be sure of having at least three red balls?
4
12
7
11
The English alphabet contains 21 consonants and 5 vowels. How many strings of four letters of the English alphabet contain exactly two consonants?
46305
2625
66150
840
The English alphabet contains 21 consonants and 5 vowels. How many strings of six English letters are there that start and end with S and contain at least one vowel, if letters can be repeated?
C(26,4) - 2*C(21,4)
([26]^4) - ([21]^4)
C(26,4) - C(21,4)
([26] ^4) - ([21]^4)*2
Let R ={(1, 1),(2, 1), (2, 3), (3, 1), (4, 2), (4, 3)}. Find R^2?
{(1, 1), (1, 2), (1, 3), (2, 4), (3, 2), (3, 4)}
{(1, 1), (2, 1), (3, 1), (4, 1), (4, 3)}
{(1, 1), (2, 1), (2, 3), (3, 1), (4, 2), (4, 3)}
{(1, 1), (2, 1), (3, 1), (4, 1)}
List the ordered pairs in the relation R from
A = (2, 3, 4) to B = (0, 1, 2, 3) where (a,b) from R if and only if a + b = 5.
{(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3),(3, 4)}
{(0, 5), (1, 4), (2, 3), (3, 2), (4, 1)}
{(2, 3), (3, 2), (4, 1)}
{(0, 0), (0, 1), (0, 2), (0, 3), (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3)}
What are the ordered pairs in the relation R represented by the directed graph shown in below digraph
R = {(1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 3), (4, 1), (4, 3)}.
R = {(1, 3), (1, 4), (2, 1), (2, 2), (3, 1), (3, 3), (4, 1), (4, 3)}.
R = {(1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1). (3, 3), (4, 1)}.
R = {(1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 3), (4, 1), (4, 3)}.
List the ordered pairs in the relation on {1, 2, 3} corresponding to the matrix
{(1, 1), (1, 3), (3, 1), (3, 3)}
{(1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2)}
{(1, 1), (2, 2), (3, 1), (3, 2), (1, 2), (1, 3)}
{(1, 1), (1, 3), (2, 2), (2, 3), (3, 1)}
Let R = { (a, b) | a > b} be a relation on the set of integers. The relation R is
non-antisymmetric and non-symmetric
non-reflexive and non-transitive
non-reflexive, antisymmetric and transitive
antisymmetric and symmetric
Let R = {(2, 1), (1, 2), (2, 2), (2, 3), (4, 4)} be a relation on (1, 2, 3, 4). The relation R is
transitive and antysimmetric
symmetric
transitive
reflexive and transitive
The English alphabet contains 21 consonants and 5 vowels. How many strings of three letters of the English alphabet contain at least one vowel?
66150
2625
10500
8315
Which of the following compound statements is a tautology?
none of mentioned
Find correct disnjunctive normal form of
none of metioned
is logically equivalent to:
Which sets are not empty?
{x | x is a even prime greater than 5}
{x | x is a multiple of 4 and is odd}
{x | x is an even number and x + 5 is even}
{x | x is a prime number less than 5 and is odd}
None of mentioned
be poset with
None of mentioned.
7
6
8
11
Which of these sets defines an equivalence relation on set A = {1, 2, 3}?
A x A
{(1, 1), (2, 2), (3, 3), (1, 3), (3, 1), (2, 3), (3, 2)}
{(1, 2), (2, 2), (3, 3)}
None of mentioned.
{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)}
Which of the following does not satisfy commutative law?
→
⋁
none of mentioned
⋀
↔
Find the remainder when
13
15
None of the mentioned.
2
1
Solve the system:
87 + 30k
177 + 210k
27 + 30k
None of the mentioned
37 + 210k
Solve the reccurrence relation
None of mentioned
Find all solutions in integers of 97x + 25y = 4.
x = 32 + 25k; y = —124 - 97k;
x = 32 - 97k; y = -124 + 25k;
x = 32 + 25k; y = 124 - 97k;
x = -32 + 97k; y = -124 - 97k;
None of the mentioned.
What is the first step of mathematical induction?
Assume that the case n = 1 is true.
Assume that everything is true.
Prove that n = k is true.
Prove the first case, usually n = 1, is true.
Prove n = k + 1 is true.
Find the prime decomposition of 2142.
2•3^2•7•17
None of the mentioned.
2•3^2•119
2^2•9•119
2•9•110
The quotient and remainder when 818 is divided by -31 are
q = 26; r = 12
q = 27;7 = 19
q = —26; r = 12
None of the mentioned.
q = -27; = 19
Find the GCD of 818 and -194.
None of the mentioned.
8
2
4
-2
Sum of two different prime numbers is:
Prime number.
Composite number.
Even number.
Either Prime or Composite.
None of the mentioned.
How many words (with or without meaning) of three distinct letters of the English
alphabets are there?
None of mentioned.
17576
2600
78
15600
Find the number of permutations of
a, b, c, ... ,x, y, z in which none of the words spin, game, or net occurs.
26! - 2 - 23! - 24! + 2 - 21!
26! — 2 • 23! — 24! + 21! + 20!
None of mentioned.
26! — 2 - 23! — 24! + 2 - 20!
26! — 2 - 23! - 24! + 2 - 20! + 21!
Find the prime decomposition of 968.
2^3•11•13
2^3•143
2^2•11•22
2^3•11^2
None of the mentioned.
A bag contains 7 red marbles, 8 white marbles, and 9 blue marbles. What is the minimum number of marbles you have to choose randomly from the bag to ensure that we get 5 marbles of same color?
12
None of mentioned.
7
5
13
Evaluate
None of mentioned.
336
40320
56
6720
Solve the reccurence relation
None of mentioned
Find the GCD of 512 and 624.
32
15
12
None of mentioned
16
Determine the coefficient of
48384
-108864
108864
None of mentioned
-48384
Find all solutions in integers of 917 + 21y=15.
None of mentioned
x =6—11k; y=-12+23k
x = -12 + 23k; y = 6 - 11k;
x = -12 - 11k; y = 6 + 23k;
x =12+23k; y=6- 11k
A bag contains 8 red marbles, 8 white marbles
None of mentioned.
6
7
9
8
Find the remainder when
4
6
1
None of the mentioned.
3
Which of the following statements is the negation of the statements "3 is odd or -8 is positive"?
"3 is odd or -8 is not negative"
"3 is even and -8 is negative"
"3 is even or -8 is not negative"
"3 is odd and -8 is not negative"
None of the mentioned.
Let A be a set with 3 elements and B be a set with 4 elements. How many elements does A × B have?
4
3
71
24
12
Which of the following compound statements is a contradiction?
None of mentioned
