A set has elements. How many relations can be defined from to ?

Answer and explanation

Correct answer: C. 33554432

  1. Step 1: A binary relation on set is defined as any subset of the Cartesian product .
  2. Step 2: With , the Cartesian product has ordered pairs.
  3. Step 3: The total number of possible subsets of a set with 25 elements is .
Answer
33554432.
Why not the others: The other numbers (10, 25, 32) confuse the number of relations with the Cartesian product size or power set of .

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