Question

Consider the set

A x x   :

is an integer,

0 4  x 

a) Write A in Roster form. (1)

b) If B = {5,6}, then write

A B . (1)

c) Write the number of possible relations

from A to B.​

Answer 1

SOLUTION

TO DETERMINE

Consider the set

A = { x : x is an integer, 0 ≤ x < 4 }

a) Write A in Roster form.

b) If B = { 5 , 6} . then write A × B

c) Write the number of possible relations from A to B.

EVALUATION

a) Here the given set is

A = { x : x is an integer, 0 ≤ x < 4 }

So the elements of A are 0 , 1 , 2 , 3

Hence A in Roster form

A = { 0 , 1 , 2 , 3 }

b) Here

A = { 0 , 1 , 2 , 3 }

B = { 5 , 6}

So

A × B = { (0,5), (0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6)}

c) We know that a relation from A to B is a subset of A × B

Here n(A×B) = 8

So the number of relations from A to B

= Number of subsets of A×B

$\sf{ = {2}^{8} }$

$\sf{ = 256}$

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Answer 2

Answer:

less than 4 means1,2,3,4,

so answer is