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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 \'SET\'}, what is A ∩ B?

Options:

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

Correct Answer: {T}

Solution: 

The intersection A ∩ B consists of common letters, which is {T}.

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 'SET'}, what is A ∩ B?
  1. {M, A, T}
  2. {A, T}
  3. {T}
  4. {}

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 'SET'}, what is A ∩ B?
  • Step 1: Identify the letters in the word 'MATH'. This gives us the set A = {M, A, T, H}.
  • Step 2: Identify the letters in the word 'SET'. This gives us the set B = {S, E, T}.
  • Step 3: Find the common letters between set A and set B. Look for letters that appear in both sets.
  • Step 4: The only letter that is in both A and B is 'T'.
  • Step 5: Therefore, the intersection A ∩ B is the set containing the common letter, which is {T}.
  • Set Theory – Understanding the concept of sets, particularly the intersection of two sets.
  • Letter Identification – Identifying letters from given words and determining common elements.
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