Free Printable DISCRETE MATH

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DISCRETE MATH

Total questions: 50

Worksheet time: 33mins

Name

Class

Date

If A = {x/x is a positive even integer less than 20}, which of the following is TRUE?

15 ∈ A

16 ∉ A

18 ∈ A

20 ∈ A

If U = {x/x is a whole number less than 20} and A = {1, 3, 5, 7, 9, 11, 13, 15, 17}. Find A^c.

{ 2, 4, 6, 8, 10, 12, 14, 16, 18 }

{ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18 }

2, 4, 6, 8, 10, 12, 14, 16, 18, 20 }

{ 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 28 }

Given: X = {1, 4, 7, 9, 11 } and Y = { 2, 4, 5, 7, 8 }, find X $\cap$ Y.

X $\cap$ Y = { }

X $\cap$ Y = { 4 }

X $\cap$ Y = { 7 }

X Y = { 4, 7 }

Given: X = { 0, 3, 6, 7, 10 } and Y = { 3, 4, 5, 7, 10 }, find X $\cup$ Y.

{ 3, 4, 5, 6, 7 }

{ 3, 4, 5, 6, 7, 10 }

{ 0, 3, 4, 5, 6, 7, 10 }

{ 0, 3, 4, 5, 6, 7, 8, 10 }

If set P and set Q are disjoints then their intersection is _____.

empty

P or Q

If set A has 3 elements, find the cardinality of its power set.

If M = {3, 5} and N = {2, 4, 6}, find M × N.

M × N = {(3, 2), (3, 4), (3, 6)}

M × N = {(3, 2), (3, 4), (3, 6), (5, 2), (5, 4)}

M × N = {(3, 2), (3, 4), (5, 2), (5, 4), (5, 6)}

M × N = {(3, 2), (3, 4), (3, 6), ((5, 2), (5, 4), (5, 6)}

Given: P = { 1, 2, 3 } and Q = { set of natural numbers between 7 and 11 }. Which of the following statements is TRUE?

P and Q are equal

P and Q are equivalent

P and Q are joint

P and Q are empty

A relation R is said to be _____ if ( a,b ) $\in$ R. and ( b, c ) $\in$ R $\rightarrow$ ( a, c ) $\in$ R

reflexive

symmetric

transitive

anti-symmetric

10.

A relation R is said to be _____ if (a,b) $\in$ R, that is aRb = bRa for all a,b $\in$ R.

reflexive

symmetric

transitive

anti-symmetric

11.

A relation R is said to be _____ if (a,a) $\in$ R for all a $\in$ A, that is every element of A is R-related to itself,

reflexive

symmetric

transitive

anti-symmetric

12.

If { 1, 3, 4, 7 } and If { 2, 5, 6, 8, 9 }. Define the relation from such that the element in plus an element in is even.

R = { (1, 5), ( 1,9), ( 3, 5), (3, 8), ( 4, 2 ), (4, 8 ), ( 7, 5), (7, 9) }

R = { (1, 5), ( 1,9), ( 3, 5), (3, 9), ( 4, 2 ), (4, 8 ), ( 7, 5), (7, 9) }

R = { (1, 5), ( 1,9), ( 3, 5), (3, 9), ( 4, 2 ), (4, 8 ), ( 7, 8), (7, 9) }

R = { (1, 6), ( 1,9), ( 3, 5), (3, 9), ( 4, 2 ), (4, 8 ), ( 7, 5), (7, 9) }

13.

13. If M = {3,5,7} and N ={6,10,17, 33,49} . Define the relation from such that the elements in when squares are less than in elements in N.

R = { (3, 10), (3,17), ( 3, 33), (3, 49), ( 5, 33 ), (5, 49 ) }

R = { (3, 10), (3,17), ( 3, 33), (3, 49), (5, 33), (5, 49), ( 7, 49) }

R = { ( 3, 6 ), (3, 10), ( 3,17), ( 3, 33), (3, 49), ( 5, 33 ), (5, 49 ) }

R = { (3, 10), ( 3,17), ( 3, 33), (3, 49), ( 5, 33 ), (5, 49 ), (9, 49) }

14.

14. What Is the cardinality of an empty?

15.

What Is the cardinality of the subset an empty set?

16.

What is the cardinality of {∅, {∅}}?

17.

If two sets are disjoint and the cardinality of sets A and B are 4 and 5 respectively. What is n(A B)?

18.

In the given Venn diagram below, what is n(R $\cap$ G) ?

19.

In the given Venn diagram below, what is n( R $\cup$ G ) ?

20.

In the given Venn diagram below, what is n( G - R ) ?

21.

Out of 50 students of BSIT cluster, 35 students like to play Mobile Legends, 25 like to play Call of Duty and 15 like to play both. How many students like to play Mobile Legends only?

22.

Out of 50 students of BSIT cluster, 35 students like to play Mobile Legends, 25 like to play Call of Duty and 15 like to play both. How many students do not like any of the two games?

23.

Which of the following is a proposition?

Sit tall!

m + n = q

Tomato is a fruit!

When is your birthday!

24.

Which of the following is not a proposition?

Open the door!

5+6 > 7

2 + 3 = 5

Roses are blue.

25.

A statement that cancels out or denies another statement or action.

negation

conjunction

disjunction

implication

26.

If the statement p and q are true then p $\wedge$ q is true otherwise it’s false.

negation

conjunction

disjunction

implication

27.

If the statement p and q are false then p $\vee$ q is false otherwise it’s true.

negation

conjunction

disjunction

implication

28.

This can be conceptualized as determining the chance of occurrence of an event.

combination

permutation

probability

factorial

29.

This refers to any subset of a sample space.

event

experiment

probability

sample space

30.

This refers to the set of all possible outcome.

event

experiment

probability

sample space

31.

If you conduct an experiment by tossing a pair of coins. The sample space is the set of:

S = {H, T}

S = {T, H}

S = {T, H, H, T}

S = {TT, HH, TH, HT}

32.

If A and B are two mutually exclusive events, where P(A) is the probability of A and P(B) is the probability of B, P(A|B) is the probability of A given that B is true. P(B|A) is the probability of B given that A is true.

Baye’s Theorem

Conditional Probability

Probability Axiom

Theory of Probability

33.

The probability for an impossible event is __________.

-1

34.

The probability for a certain event is __________.

-1

cannot be determined

35.

The total possible outcomes for a pair of dice is __________.

36.

What is N in the sequence 1, 1, 2, 3, 5, 8, 13, 21, 34, N?

37.

What is the common ratio in the sequence 64, 16, 4, 1, …?

- 4

1/4

- 1/4

38.

What is the 27^th term of the sequence 100, 95, 90, … ?

-30

-40

39.

Which useful number diagram can also be used to generate a list of Fibonacci numbers?

Polo’ Triangle

Pierre’s Triangle

Pascals's Triangle

Pentagram’s Triangle

40.

What is the value of $F_{20}$ ?

6765

7765

10945

11945

41.

What is the first 3-digit perfect square number that appears on the list of Fibonacci numbers?

100

121

144

169

42.

Strict graph is another name for which graph?

null grapg

multi-graph

simple graph

regular graph

43.

. (I) .A graph is connected if any two vertices of the graph are connected by a path.

(II) A graph is disconnected if at most two vertices of the graph are not connected by a path.

statement I is TRUE and statement II is FALSE

statement II is TRUE and statement I is FALSE

both statements are true

both statements are false

44.

I) A graph is regular if the vertices of the graph different degree.

(II) A graph is called complete graph if every two vertices pair are joined by exactly one edge.

statement I is TRUE and statement II is FALSE

statement II is TRUE and statement I is FALSE

both statements are true

both statements are false

45.

If two graphs G and H contain the same number of vertices connected in the same way, they are called

planar graph

non-planar graph

isomorphic graph

non-isomorphic graph

46.

What is the degree of the given graph ?

47.

Empty tree is another name for

labeled tree

unlabeled tree

rooted tree

unrooted tree

48.

An n-vertex graph has ______ edges.

n - 1

n - 2

n - 3

49.

A graph which consists of disjoint union of trees is called

labeled tree

rooted tree

forest

catterpillar tree

50.

(I) The center of a tree is a vertex with minimal eccentricity.

(II) The maximum eccentricity is the tree diameter.

statement I is TRUE and statement II is FALSE

statement II is TRUE and statement I is FALSE

both statements are TRUE

both statements are FALSE

100 %

DISCRETE MATH

Total questions: 50

Worksheet time: 33mins

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