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From the sets , given below , select exa...

From the sets , given below , select examples of equal sets :
`A={2,4,12},B={1,2,3,4}`
`C={4,8,12,14},D={3,1,4,2}`
`E={-1,1},F={0,0}`,
`G={1,-1},H={0,1}`.

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The correct Answer is:
To determine which of the given sets are equal sets, we need to recall that two sets are considered equal if they contain exactly the same elements, regardless of the order or repetition of those elements. Let's analyze the sets one by one: 1. **Set A**: \( A = \{2, 4, 12\} \) 2. **Set B**: \( B = \{1, 2, 3, 4\} \) - **Comparison**: The elements of set A are 2, 4, and 12, while the elements of set B are 1, 2, 3, and 4. Since they do not contain the same elements, \( A \neq B \). 3. **Set C**: \( C = \{4, 8, 12, 14\} \) 4. **Set D**: \( D = \{3, 1, 4, 2\} \) - **Comparison**: The elements of set C are 4, 8, 12, and 14, while the elements of set D are 3, 1, 4, and 2. Since they do not contain the same elements, \( C \neq D \). 5. **Set E**: \( E = \{-1, 1\} \) 6. **Set F**: \( F = \{0, 0\} \) - **Comparison**: Set E contains -1 and 1, while set F contains only 0 (even though it is repeated). Since they do not contain the same elements, \( E \neq F \). 7. **Set G**: \( G = \{1, -1\} \) 8. **Set H**: \( H = \{0, 1\} \) - **Comparison**: Set G contains 1 and -1, while set H contains 0 and 1. Since they do not contain the same elements, \( G \neq H \). Now, let's summarize the findings: - Sets A and B are not equal. - Sets C and D are not equal. - Sets E and F are not equal. - Sets G and H are not equal. However, we notice that sets B and D actually contain the same elements (1, 2, 3, 4) but in different orders. Therefore, we can conclude that: - **Equal Sets**: \( B = D \) ### Final Answer: The equal sets are \( B \) and \( D \).
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