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24 September, 03:34

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.

+1
Answers (2)
  1. 24 September, 03:48
    0
    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
  2. 24 September, 04:03
    0
    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 = ...
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