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How many relations can be formed from a set with 3 elements?
How many relations can be formed from a set with 3 elements?
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Practice Questions
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Q1
How many relations can be formed from a set with 3 elements?
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The number of relations on a set with n elements is 2^(n^2). For n = 3, it is 2^(3^2) = 2^9 = 512.
Questions & Step-by-step Solutions
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Q
Q: How many relations can be formed from a set with 3 elements?
Solution:
The number of relations on a set with n elements is 2^(n^2). For n = 3, it is 2^(3^2) = 2^9 = 512.
Steps: 7
Show Steps
Step 1: Understand what a set is. A set is a collection of distinct objects. In this case, we have a set with 3 elements.
Step 2: Identify the number of elements in the set. Here, n = 3.
Step 3: Know the formula for the number of relations on a set. The formula is 2^(n^2).
Step 4: Calculate n^2. Since n = 3, we calculate 3^2, which equals 9.
Step 5: Substitute n^2 into the formula. We now have 2^(3^2) = 2^9.
Step 6: Calculate 2^9. This equals 512.
Step 7: Conclude that the number of relations that can be formed from a set with 3 elements is 512.
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