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If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the

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Question: If A = {x | x is a letter in the word \'MATH\'} and B = {x | x is a letter in the word \'SCIENCE\'}, what is A ∩ B?

Options:

  1. {A}
  2. {M, A, T}
  3. {A, C, E}
  4. {A, T}

Correct Answer: {A}

Solution: 

The intersection A ∩ B includes letters that are common in both words. The only common letter is \'A\', so A ∩ B = {A}.

If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the

Practice Questions

Q1
If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the word 'SCIENCE'}, what is A ∩ B?
  1. {A}
  2. {M, A, T}
  3. {A, C, E}
  4. {A, T}

Questions & Step-by-Step Solutions

If A = {x | x is a letter in the word 'MATH'} and B = {x | x is a letter in the word 'SCIENCE'}, what is A ∩ B?
  • Step 1: Identify the letters in the word 'MATH'. The letters are M, A, T, H. So, A = {M, A, T, H}.
  • Step 2: Identify the letters in the word 'SCIENCE'. The letters are S, C, I, E, N, C, E. So, B = {S, C, I, E, N}.
  • Step 3: Find the common letters between sets A and B. Compare the letters in A with those in B.
  • Step 4: The only letter that appears in both sets A and B is 'A'.
  • Step 5: Therefore, the intersection A ∩ B is {A}.
  • Set Intersection – Understanding how to find common elements between two sets.
  • Letter Identification – Identifying letters from given words to form sets.
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