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Class 10MathematicsSetsPower Set and SubsetsMediumLevel 8

If A ⊆ B, B ⊆ C, and A ≠ C, which statement is always true?

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Answer and explanation

Correct answer: A ⊂ C; A is a proper subset of C

Subset inclusion is transitive: from A ⊆ B and B ⊆ C, we obtain A ⊆ C. The additional condition A ≠ C rules out equality, so A must be a proper subset of C, written A ⊂ C. Nothing in the conditions forces B to equal either A or C, so options B and C are not always true.

Tags

setssubset_transitivityproper_subsetset_relationsPower Set and SubsetsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A ⊂ C; A is a proper subset of C

Why is this the correct answer?

Subset inclusion is transitive: from A ⊆ B and B ⊆ C, we obtain A ⊆ C. The additional condition A ≠ C rules out equality, so A must be a proper subset of C, written A ⊂ C. Nothing in the conditions forces B to equal either A or C, so options B and C are not always true.

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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