There are 32,768 binary relations from set A = {a, b, c} to set B = {0, 1, 2, 3, 4}. This conclusion is derived from the fact that a binary relation is defined as a subset of the Cartesian product A × B. Given that A has 3 elements and B has 5 elements, the total number of ordered pairs in A × B is 15. Since each ordered pair can either be included in a relation or not, the total number of subsets, which represents the binary relations, is calculated as 2^15 = 32,768.
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ktheo said:Homework Statement
True or False: Given that A = {a,b,c} and B={0,1,2,3,4}, there are 32768 binary relations from A to B
I assume there is some simple way to tell how many relations there are given two different sets, but I don't know it. Factorials? Powers? I'm not sure what.
ktheo said:Homework Statement
True or False: Given that A = {a,b,c} and B={0,1,2,3,4}, there are 32768 binary relations from A to B
I assume there is some simple way to tell how many relations there are given two different sets, but I don't know it. Factorials? Powers? I'm not sure what.