discrete math

Question 1

unordered collectrion of OBJECTS

Answer 1

SET

Question 2

OBJECTS THAT BELONG TO A SET IS CALLED?

Answer 2

ELEMENTS

Question 3

THE IDENTIFIER OF A GROUP OF OBJECT TO BE CALLED A SET

Answer 3

{} CURLY BRACKETS

Question 4

3 WAYS TO RESPRESENT THE ELEMENTS IN A SET

Answer 4

DESCRIBE THE ELEMENTS
LIST THE ELEMENTS
IDENTIFIER TO REPRESENT THE ELEMENTS

Question 5

2 SPECIAL SETS

Answer 5

UNIVERSAL SET- SET OF ALL THE OBJECTS UNDER DISCUSSION.
EX– U=(1,2,3,4,5}
NULL SET- SET CONTAINING NO ELEMENTS THAT IS PART OF THE UNIVERSAL SET
Φ={}

Question 6

4 RELATIONSHIPS OF SETS

Answer 6

EQUALITY= 2 SETS ARE SAID TO BE EQUAL IF AND ONLY IF THEY HAVE THE SAME DISTINCT ELEMENTS
(NO. OF ELEMENTS DOES NOT FACTOR TO EQUALITY)
A=C

SUBSET= ALL ELEMENTS OF A SET ARE ALSO ELEMENTS OF ANOTHER SET.
D⊆A

PROPER SUBSET=F SET 2 CONTAINS AT LEAST 1 ELEMENT THAT IS NOT PRESENT IN SET 1
⊂⊂⊂⊂⊂⊂⊂

DISJOINT- IF 2 SETS HAVE NO COMMON ELEMENTS

Question 7

5 OPERATIONS ON SET

Answer 7

INTERSECTION ∩

UNION U [similar elements does not repeat]

DIFFERENCE (-) or () elements that are is set 1 but
nott in set 2 (remove similar sets)

SYMMEETRIC DIFFERENCE- DIFFERENCE OF THE UNION AND INTERSECTION OF TWO SETS
A∆B= (AUB)-(A∩B)

COMPLEMENT- DIFFERENCE OF THE UNIVERSAL SET AND A SPECIFIC SET.
(A^C OR A’ )

you can illustrate these in a venn diagram

Question 8

A SET OF RELATION BETWEEN TWO SETS WHERE IT MAPS THE ELEMENTS OF SET A WITH ONE AND ONLY ONE ELEMENTS OF SET B

Answer 8

FUNCTION-

A function is a relation in which each possible input value leads to exactly one output value. We say “the output is a function of the input.” The input values make up the domain, and the output values make up the range.

Question 9

in a function, what do you call the SET of actual inputs where the codomain is paired with a domain.

Answer 9

RANGE

Question 10

3 TYPES OF FUNCTION

Answer 10

INJECTIVE - (1TO1 FUNCTION) EACH ELEMENT OF THE SET B ARE PAIRED WITH A DISTINCT ELEMENT IN SET A

SURJECTIVE- (ONTO) ALL ELEMENTS OF THE CODOMAIN ARE PAIRED WITH AN ELEMENTS IN THE SET A
BIJECTIVE (ONE TO ONE & ONTO) ALL ELEMENTS OF THE SET B ARE PAIRED WITH A DISTINCT ELEMENT IN SET A

Question 11

2 OPERATIONS OF FUNCTIONS ONLY APPLICABLE FOR FUNCTIONS

Answer 11

INVERSE FUNCTION
Y=F(X) —> X=G(Y)

COMPOSITION FUNCTION- APPLYING ONE FUNCTION TO THE RESULT OF ANOTHER FUNCTION
F(G(X)) — EX

Question 12

SHAPE THAT REPRESENT THE UNIVERSAL SET

Answer 12

RECTANGLE

Question 13

SHAPE THAT REPRESENT THE SUBSET OF A UNIVERSALSET

Answer 13

CIRCLE

Question 14

product of two sets in pairs that contains all ordered pairs

Answer 14

CARTESIAN PRODUCT “product”

A X B =

Question 15

A SUBSET OF THE CARTESIAN PRODUCT

Answer 15

RELATION

Question 16

5 PROPERTIES OF RELATION

Answer 16

REFLEXIVE - ALL ELEMENTS OF A RELATION SHOULD have (a,a) of every (a) that is an element of set A;

ex; A={1,2,3}, then R is reflexive if (1,1)(2,2), & (3,3) all exist in the relation

IRREFLEXIVE- No any (a,a) pair in the relation

SYMMETRIC- [a pair is symmetric if (a,b) & (b,a) exist in the relation]. a relation can be alled symmetric relation if all the elements are symmetric.

ANTISYMMETRIC- all “symmtric” pairs should satisfy (a=b) to be called antisymmetric relation.

TRANSITIVE- if (a,b) & (b,c) are elements in the relation. then (a,c) is an element of the relation.
ex: {(1,1)(2,1)(1,2)} is trasitive since;
if 12 is AB, then BC can be= 21, so that AC=11 which all exists in the relation
note- you just need to use all elements in pairing for it to be transitive.