Question

5. How many one-to-one correspondences are there between the sets {a,b,c,d} and {1,2,3,4} if in each sequence
a. b must correspond to 3
b. b must correspond to 3 and d to 4
c. a and c must correspond to even numbers.

Answer 1

a. if A={a,b,c,d} and B={1,2,3,4}, b must correspond to 3, so just to calculate one-to-one correspondences from {a,c,d} to {1,2,4}. use formula (n(B))^((n(A)) = 3^3 = ....

Answer 2

27?

Answer 3

right

Answer 4

okay and how would i do the other two?

Answer 5

b must correspond to 3 and d to 4,
so remainder elements of set A is {a,c} and B is {1,2}
just calculate of 2^2 = ...

Answer 6

okay, i got that one right then. So far just the first one i got wrong. are you sure its 27? and how would you do the last one?

Answer 7

yea, a. 3^3 = 27
b. 2^2 = ...
c. is it permutation ?

Answer 8

Do u know permutation ?

Answer 9

no, idk what that is yet..

Answer 10

ok, nope... it's a topic in maths about combinatorica or prabability
so, i think it is not permutation and for the last one u know that if a pair to 2 then c pair to 4. what are elements remainder of set A and set B?

Answer 11

4?

Answer 12

bd13

Answer 13

yes, true...
bd13 ?

Answer 14

b, d, 1, 3 are left

Answer 15

yups...
:)

Answer 16

mmm, okay. So a. 27 b. 4 c. ...?

Answer 17

like part b

Answer 18

Can you explain to me how to do "c"?

Answer 19

if u use manual :
if a->2 and c->4, there are 2 possible ways to pairs for domain b and d, are
(a,2),(c,4),(b,1),(d,3) or (a,2),(c,4),(b,3),(d,1)
if a->4 and c->2, there are 2 possible ways to pairs for domain b and d, are
(a,4),(c,2),(b,1),(d,3) or (a,2),(c,4),(b,3),(d,1).
so, the total way = 4 ways

Answer 20

So it's just like part B? I really appreciate it.

Answer 21

yups, but i was use permutation's concept before...
but manual work also

Answer 22

can u do part b, by manual ?

Answer 23

We're using permutations.

Answer 24

yea, easier using by permutations

Answer 25

*Note: List all of the correspondences for each problem (i.e. b → 3, a → 1, etc.)

Answer 26

(b,3),(a,1),(c,2),(d,4) or (b,3),(a,1),(c,4),(d,2)

Answer 27

Can you do a. And b like that for me?