Question 4: (Math Question) Number of Reflexive Relations What is the possible number of...
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Question 4: (Math Question) Number of Reflexive Relations
What is the possible number of reflexive relations on a set of 5 elements?
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Answer: B. B) 2^20
The number of reflexive relations on a set of n elements is 2^(n^2 - n). For n = 5, 2^(25 - 5) = 2^20.
Step-by-step Derivation:
Step 1: Total pairs in a set of n elements = n^2.
Step 2: A reflexive relation must contain all n diagonal pairs (x, x).
Step 3: The remaining n^2 - n non-diagonal pairs can either be included or excluded independently.
Step 4: Number of reflexive relations = 2^(n^2 - n) = 2^(25 - 5) = 2^20.