Sets & Relation (Part 2)

Question 1

It is invented by John Venn, is a schematic diagram that shows all possible logical relations between different mathematical sets.

Answer 1

Venn Diagram

Question 2

Set Operations include:

A. Set Union, Set Intersection, Set Difference, Complement of Set, and Cartesian Product.

B. Set Union, Set Intersection, Equivalent Set, Cartesian Product

C. Set Intersection, Set Difference, Complement of Set and Cartesian Product

Answer 2

A

Question 3

Is the set of elements which are in A, in B, or in both A and B. (denoted by U).

A. Set Union
B. Set Intersection
C. Set Difference
D. Complement of a Set

Answer 3

A. Set Union

EXAMPLE! − If A={10,11,12,13}
and B = {13,14,15}

then A ∪ B={10,11,12,13,14,15}
(The common element(13) occurs only once)

Question 4

A type of SET OPERATION denoted by ∩

A. Set Union
B. Set Intersection
C. Set Difference
D. Complement of a Set

Answer 4

B. Set Intersection

Example − If A={11,12,13}
and B={13,14,15}

then A ∩ B={13}

Question 5

A set of elements which are only in A but not in B denoted like this (A - B)

A. Set Union
B. Set Intersection
C. Set Difference
D. Complement of a Set

Answer 5

Set Difference

Question 6

Set of operations that is (denoted by A′)

A. Set Union
B. Set Intersection
C. Set Difference
D. Complement of a Set

Answer 6

D. Complement of a Set

EXAMPLE!
Universal set: U= {1,2,3,4,5,6,7,8,9,10}
Subset A:A={2,4,6,8,10}

PARA DALI MASABTAN YWAA KA!!
A’ = ( U - A )
A’ = (1, 3 ,5, 7, 9,)

Question 7

It is defined as all possible ordered pairs. (A x B)

A. Set Union
B. Set Intersection
C. Set Difference
D. Cartesian Product

Answer 7

D. Cartesian Product

EXAMPLE!

A = { a, b}, B = {1, 2}
therefore
A x B = { ( a, 1), (a, 2), (b, 1), (b, 2) }
B × A ={ (1, a), (1, b), (2, a), ( 2 , b ) }

Question 8

It is the set of all subsets of S including the empty set, denoted as P(S).

A. Proper Subset
B. Power Set
C. Subset
D. Partitioning of a Set

Answer 8

B. Power Set

Question 9

It is a collection of n disjoint subsets

A. Proper Subset
B. Power Set
C. Subset
D. Partitioning of a Set

Answer 9

D. Partitioning of a Set

Question 10

________ represents the number of ways to partition a set

A. Partitioning of a Set
B. Power Set
C. Subset
D. Bell Numbers

Answer 10

D. Bell Numbers

Question 11

_________ may exist between objects of the same set or between objects of two or more sets.

Answer 11

Relations

Question 12

is a subset of the Cartesian product x × y.

A. Binary Relation
B. Domain
C. Range
D. n - ary Relation

Answer 12

A. Binary Relation

Question 13

Is a relation that involves sets and consists of 3 sets different from Binary which consists of 2 sets only

A. Binary Relation
B. Domain
C. Range
D. n - ary Relation

Answer 13

D. n - ary Relation

Question 14

Identify what type of graph which a relation can be represented?

Answer 14

Directed Graph

Question 15

What type of relation is this example:

R = {(1,2),(2,3)}, then
R′ = {(2,1),(3,2)}

A. Inverse Relation
B. Identity Relation
C. Symmetric
D. Transitive

Answer 15

A. Inverse Relation

Question 16

What type of relation is this example: Let S be the set and I be the relation

S = {1, 2, 3}
I = { (1,1), (2,2), (3,3) }

A. Inverse Relation
B. Identity Relation
C. Symmetric
D. Transitive

Answer 16

B. Identity Relation

Question 17

What type of relation is this example:

I = { (1, 2), (2, 1), (3, 2), (2, 3) }

A. Inverse Relation
B. Identity Relation
C. Symmetric
D. Transitive

Answer 17

C. Symmetric