Question

Determine how many one-to-one correspondences are possible between two sets, {n,t,z,w,v} and {1,2,3,4,5}, given the following conditions.

a. If in each correspondence n must match with 2.
b. If in each correspondence n must match with 2 and t must match with 1.
c. If in each correspondence n, t, z must match with an odd number.

Answer 1

There are 3 one-to-one correspondences between the sets {n,t,z,w,v} and {1,2,3,4,5}, satisfying the given conditions.

Step-by-step explanation:

In this question, we are given two sets: {n,t,z,w,v} and {1,2,3,4,5}. We need to find the number of one-to-one correspondences between these sets, satisfying certain conditions. Let's go through each condition one by one:

a. If n must match with 2, then we have only one possibility for the correspondence, which is n=2.

b. If n must match with 2 and t must match with 1, then we have again only one possibility, which is n=2 and t=1.

c. If n, t, and z must match with an odd number, then there are 3 odd numbers in the second set which can be matched with {n,t,z}. Therefore, for each possible value of n (which is 1), there are 3 possible correspondences.

So, the total number of one-to-one correspondences between the two sets, satisfying these conditions, is 1 (from condition a) multiplied by 1 (from condition b) multiplied by 3 (from condition c), which equals 3.