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In a certain mathematical context, if 'A' is a subset of 'B', which of the follo

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Question: In a certain mathematical context, if \'A\' is a subset of \'B\', which of the following is necessarily true?

Options:

  1. B is a subset of A.
  2. A and B are equal.
  3. Every element of A is also an element of B.
  4. B contains no elements.

Correct Answer: Every element of A is also an element of B.

Solution: 

If A is a subset of B, it means that every element of A is contained within B.

In a certain mathematical context, if 'A' is a subset of 'B', which of the follo

Practice Questions

Q1
In a certain mathematical context, if 'A' is a subset of 'B', which of the following is necessarily true?
  1. B is a subset of A.
  2. A and B are equal.
  3. Every element of A is also an element of B.
  4. B contains no elements.

Questions & Step-by-Step Solutions

In a certain mathematical context, if 'A' is a subset of 'B', which of the following is necessarily true?
  • Step 1: Understand what a subset means. A subset is a set where all its elements are also in another set.
  • Step 2: Identify the sets involved. Here, we have set A and set B.
  • Step 3: Recognize the relationship. If A is a subset of B, it means every element in A is also found in B.
  • Step 4: Conclude that if you pick any element from A, it will definitely be in B.
  • Set Theory – Understanding the relationship between sets, specifically the definition of subsets.
  • Subset Definition – A subset is defined as a set where all its elements are also elements of another set.
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