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If A = {x | x is an even integer} and B = {x | x is a multiple of 4}, what is A

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Question: If A = {x | x is an even integer} and B = {x | x is a multiple of 4}, what is A ⊆ B?

Options:

  1. True
  2. False
  3. Depends on x
  4. None of the above

Correct Answer: False

Solution: 

A is the set of all even integers, while B is the set of multiples of 4. Not all even integers are multiples of 4 (e.g., 2 is even but not a multiple of 4), hence A is not a subset of B.

If A = {x | x is an even integer} and B = {x | x is a multiple of 4}, what is A

Practice Questions

Q1
If A = {x | x is an even integer} and B = {x | x is a multiple of 4}, what is A ⊆ B?
  1. True
  2. False
  3. Depends on x
  4. None of the above

Questions & Step-by-Step Solutions

If A = {x | x is an even integer} and B = {x | x is a multiple of 4}, what is A ⊆ B?
  • Step 1: Understand what set A is. A is the set of all even integers, which includes numbers like -4, -2, 0, 2, 4, 6, etc.
  • Step 2: Understand what set B is. B is the set of all multiples of 4, which includes numbers like -8, -4, 0, 4, 8, etc.
  • Step 3: Determine if every element in set A is also in set B. This means checking if every even integer is a multiple of 4.
  • Step 4: Find an example of an even integer that is not a multiple of 4. For instance, the number 2 is even but not a multiple of 4.
  • Step 5: Since we found an even integer (2) that is not in set B, we conclude that not all elements of A are in B.
  • Step 6: Therefore, we can say that A is not a subset of B, which means A ⊆ B is false.
  • Set Theory – Understanding the definitions of sets, subsets, and the relationships between different sets.
  • Even Integers vs. Multiples of 4 – Recognizing that while all multiples of 4 are even, not all even integers are multiples of 4.
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