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

b --> 3
d --> 4
a, c--> 2 or 4

if a --> 2 then
c --> 4
b --> 3
d --> 4
Number of one-to-one correspondences is 2.

if a --> 4 then
c --> 2
b --> 3
d --> 4
Number of one-to-one correspondences is 2.

2 + 2 = 4 one-to-one correspondences