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Given sets A = {2, 4, 6, 8} and B = {4, 6, 10, 12}, what is the Jaccard similarity?

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NLP - Text Similarity and Search
Given sets A = {2, 4, 6, 8} and B = {4, 6, 10, 12}, what is the Jaccard similarity?
A0.25
B0.33
C0.5
D0.4
Step-by-Step Solution
Solution:

  1. Step 1: Find intersection

    Intersection of A and B is {4, 6}, size = 2.

  2. Step 2: Find union

    Union of A and B is {2, 4, 6, 8, 10, 12}, size = 6.

  3. Step 3: Calculate Jaccard similarity

    Jaccard similarity = intersection size / union size = 2 / 6 = 0.333..., which matches 0.33.

  4. Final Answer:

    0.33 -> Option B

  5. Quick Check:

    Intersection 2, union 6, ratio 0.33 [OK]
Quick Trick: Similarity = intersection size / union size [OK]
Common Mistakes:
MISTAKES
  • Miscounting union elements
  • Confusing intersection with union size
  • Rounding errors

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