Question

Divisibility question !

Answer 1

Let it be the sets A = {0, 1, 2, 3, 4} and B = {0, 1, 2, 3}. Write the list of ordered pairs belonging relation R from A to B as defined in the (a,b)E R , if and only if:
d) a | b
e) cmmdc(a,b) = 1
f) cmmmc(a,b) = 2.

Answer 2

If a|b then b|a =>a!=0 IS THIS CORRECT ?!

Answer 3

@ganeshie8 ?

Answer 4

asked for order pair so you don't need to get a formula.
(0,1)(0,2)(0,3)(1,1)(2,1)(2,2)(3,1)(3,3).

Answer 5

??
@ganeshie8 any idea

Answer 6

whats `cmmdc(a,b)` ?

Answer 7

Greatest common divisor

Answer 8

and cmmmc is least common multiple

Answer 9

for part a, use below :

1) \(n~ | ~0\) `every number divides 0`

2) \(1 ~|~ n\) `1 divides every number`

3) \(n~|~n\) `every number divides itself`

Answer 10

If a|b then b/a=integer =>a!=0

Answer 11

A = {0, 1, 2, 3, 4} and B = {0, 1, 2, 3}.

yes you're right, i think we don't want to divide by 0, start with 1 :

since we know that 1 divides every number, we get below ordered pairs in relation :
(1,0), (1,1), (1,2),),(1,3)

Answer 12

next see what numbers are divisible by 2 :
(2,0), (2, 2)

Answer 13

for numbers divisible by 3 you get :
(3,0), (3,3)

Answer 14

for numbers divisible by 4 you get :
(4, 0)

Answer 15

Overall below ordered pairs should satisfy part a :
```
(1,0), (1,1), (1,2),),(1,3)
(2,0), (2, 2)
(3,0), (3,3)
(4, 0)
```

Answer 16

check if we missed any ..

Answer 17

thx ganeshie
you missed nothing

Answer 18

now for gcd and lcm ?!

Answer 19

gcd(a,b)=1=>{1|a and 1|b}

Answer 20

@ganeshie8 is n | 0 valid?

Answer 21

heyy sry was afk, still here ?

Answer 22

@OOOPS i think so

Answer 23

for gcd(a,b)=1 use below :

1) gcd(n, 0) = gcd(0, n) = n
2) gcd(0, 0) = 0
3) gcd(n, n) = n

Answer 24

gcd(a,b)=1
R={(0,1),(1,0),(1,1),(1,2),(1,3),(2,1),(2,3),(3,1),(3,2),(4,1),(4,2),(4,3)}
@ganeshie8 Am I right ?

Answer 25

(3,4)

Answer 26

other than that looks good!

Answer 27

there's no (3,4)

Answer 28

look at B set

Answer 29

Oops sorry yes you're right !

Answer 30

gcd(4,2 )=2 why !?

Answer 31

(4,2) has 2 comune divisors 1 and 2 and the greatest is 2

Answer 32

@ganeshie8

Answer 33

so you want to find the gcd of 4 and 2

Answer 34

what are the divisors of 4 ?

Answer 35

1,2,4

Answer 36

what are the divisors of 2 ?

Answer 37

1,2

Answer 38

are there any common factors ?

Answer 39

1,2

Answer 40

and 2 is the largest among them, yes ?

Answer 41

yup

Answer 42

so 2 the `g`reatest `c`ommon `d`ivosor of 4 and 2
(loosely speaking)

Answer 43

as for lcm(a,b)=2
R={(1,1),(1,2),(2,1),(2,2)}

Answer 44

?

Answer 45

hows lcm(1,1) = 2 ?

Answer 46

sorry my bad

Answer 47

R={(1,2),(2,1),(2,2)}

Answer 48

looks good to me