Discrete Structures Week 8

Question 1

map of function

Answer 1

V- x C- A, E! y C- B such that f(x) = y

Question 2

image of f

Answer 2

= {f(x) | x C- A} c_ B

Question 3

pre-image/inverse image (of y C- B)

Answer 3

f^-1(y) = {x C- A | f(x) = y}

Question 4

surjection

Answer 4

if Im(f) = B

V- y C- B, f^-1(y) != empty set
V- y C- B, Ex C- A such that f(X) = y

each element in codomain has a preimage

Question 5

injection

Answer 5

given x1, x2 C- A, if x1 != x2 then f(x1) != f(x2)

f(x1) = f(x2) then x1 = x2

different elements in domain, have different images

Question 6

Cartesian Plane

Answer 6

A x B = { (x,y) | x C- R, y C- R}

Question 7

Injection and Surjection with coordinates problems

Answer 7

:)

Question 8

bijection

Answer 8

injection and surjection

Question 9

composition

Answer 9

f: x->y
g: y -> z-

composition is
gof : x -> z-
x->g(x)

Question 10

cardinality

Answer 10

of a set S is its number of elements denoted by |S|

Question 11

relationship between bijection and cardinality

Answer 11

f: A-> B is bijection
|A| = |B|

Question 12

aleph zero

Answer 12

the cardinality of the set of natural numbers
-denoted by…

Question 13

countable

Answer 13

if S is either a finite set or |S| = |N|