If A = {1, 2, 3, 4} and C = {2, 4}, why is C ⊂ A true?
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Answer and explanation
Correct answer: Every element of C is in A, and A ≠ C.
To prove that C is a proper subset of A, two conditions must be checked. First, every element of C must belong to A; here both 2 and 4 are in A. Second, C must not equal A; C lacks 1 and 3, so C ≠ A. Therefore C ⊂ A. Merely having fewer elements does not guarantee inclusion.
Frequently asked questions
What is the correct answer to this question?
Every element of C is in A, and A ≠ C.
Why is this the correct answer?
To prove that C is a proper subset of A, two conditions must be checked. First, every element of C must belong to A; here both 2 and 4 are in A. Second, C must not equal A; C lacks 1 and 3, so C ≠ A. Therefore C ⊂ A. Merely having fewer elements does not guarantee inclusion.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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