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Questions › DSE › DSE 2012 › Q18
1 markMathematics › Sets, relations and functions › Sets and set operationsHardabout 3 min

DSE 2012 Question 18: Sets, relations and functions

AAA and BBB are two non empty sets. A−B={x∈A∣x∉B}A-B=\{x\in A\mid x\notin B\}A−B={x∈A∣x∈/B} and A+B=(A−B)∪(B−A)A+B=(A-B)\cup(B-A)A+B=(A−B)∪(B−A). Consider the following statements; Statement 1: A+B=BA+B=BA+B=B implies A⊆BA\subseteq BA⊆B. Statement 2: A+B=∅A+B=\emptysetA+B=∅ implies A=BA=BA=B. Statement 3: A+B=A∪BA+B=A\cup BA+B=A∪B implies A∩B=∅A\cap B=\emptysetA∩B=∅. How many of the above statements are correct?

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A and B are two non empty sets. A-B={x∈ A| x∉ B} and A+B=(A-B)∪(B-A). Consider the following statements; Statement 1: A+B=B implies A⊆ B. Statement 2: A+B=∅ implies A=B. Statement 3: A+B=A∪ B implies A∩ B=∅. How many of the above statements are correct? (A) 0 (B) 1 (C) 2 (D) 3

Also written as: A and B are two non empty sets. A-B={x in A| x not in B} and A+B=(A-B) union (B-A). Consider the following statements; Statement 1: A+B=B implies A subseteq B. Statement 2: A+B={} implies A=B. Statement 3: A+B=A union B implies A intersection B={}. How many of the above statements are correct?

Sets, relations and functions has come up 65 times in 6 exams since 2004.

What this question tests

This question is on Sets and set operations, part of Sets, relations and functions in Mathematics.

Unions, intersections, complements and differences of sets, and the identities that connect them.

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Question from the DSE 2012 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.