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.

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 = ...

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