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If A = {1, 2, 3} and B = {2, 3, 4}, what is |A ∩ B|?

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Question: If A = {1, 2, 3} and B = {2, 3, 4}, what is |A ∩ B|?

Options:

  1. 1
  2. 2
  3. 3
  4. 0

Correct Answer: 2

Solution: 

A ∩ B = {2, 3}, so |A ∩ B| = 2.

If A = {1, 2, 3} and B = {2, 3, 4}, what is |A ∩ B|?

Practice Questions

Q1
If A = {1, 2, 3} and B = {2, 3, 4}, what is |A ∩ B|?
  1. 1
  2. 2
  3. 3
  4. 0

Questions & Step-by-Step Solutions

If A = {1, 2, 3} and B = {2, 3, 4}, what is |A ∩ B|?
Correct Answer: 2
  • Step 1: Identify the sets A and B. A = {1, 2, 3} and B = {2, 3, 4}.
  • Step 2: Find the intersection of sets A and B. The intersection (A ∩ B) includes elements that are in both sets.
  • Step 3: Look at the elements in A: 1, 2, 3 and in B: 2, 3, 4.
  • Step 4: Identify the common elements in both sets. The common elements are 2 and 3.
  • Step 5: Write the intersection as a new set. A ∩ B = {2, 3}.
  • Step 6: Count the number of elements in the intersection set {2, 3}. There are 2 elements.
  • Step 7: Write the final answer. |A ∩ B| = 2.
  • Set Intersection – The intersection of two sets A and B, denoted A ∩ B, is the set of elements that are common to both A and B.
  • Cardinality of a Set – The cardinality of a set, denoted |S|, is the number of elements in the set S.
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