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Questions › DSE › DSE 2004 › Q1
2 marks, −1Mathematics › Sets, relations and functions › Sets and set operationsHardabout 3 min

DSE 2004 Question 1: Sets, relations and functions

Consider sets AAA, BBB and CCC, and the following propositions: (i) If (A∪B)∩(A∪C)=∅(A\cup B)\cap(A\cup C)=\varnothing(A∪B)∩(A∪C)=∅, then B∩C=∅B\cap C=\varnothingB∩C=∅. (ii) If (A∩B)∪(A∩C)=∅(A\cap B)\cup(A\cap C)=\varnothing(A∩B)∪(A∩C)=∅, then B∩C=∅B\cap C=\varnothingB∩C=∅.

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Consider sets A, B and C, and the following propositions: (i) If (A∪ B)∩(A∪ C)=∅, then B∩ C=∅. (ii) If (A∩ B)∪(A∩ C)=∅, then B∩ C=∅. (A) Both propositions are true (B) Only proposition (i) is true (C) Only proposition (ii) is true (D) Both propositions are false

Also written as: Consider sets A, B and C, and the following propositions: (i) If (A union B) intersection (A union C)={}, then B intersection C={}. (ii) If (A intersection B) union (A intersection C)={}, then B intersection C={}.

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 2004 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.