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Questions › DSE › DSE 2017 › Q21
2 marks, −0.666666666666667Mathematics › Sets, relations and functions › Sets and set operationsVery Hardabout 5 min

DSE 2017 Question 21: Sets, relations and functions

Let A={(x,y)∈R2∣x≥0, y≥0, xy≥1}A=\{(x,y)\in\mathbb{R}^2\mid x\ge 0,\,y\ge 0,\,xy\ge 1\}A={(x,y)∈R2∣x≥0,y≥0,xy≥1} and B={(x,y)∈R2∣x≤0, y≥0, xy≤−1}B=\{(x,y)\in\mathbb{R}^2\mid x\le 0,\,y\ge 0,\,xy\le -1\}B={(x,y)∈R2∣x≤0,y≥0,xy≤−1}, and let C={a+b∣a∈A, b∈B}C=\{a+b\mid a\in A,\,b\in B\}C={a+b∣a∈A,b∈B}. Then

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Let A={(x,y)∈ℝ²| x≥ 0, y≥ 0, xy≥ 1} and B={(x,y)∈ℝ²| x≤ 0, y≥ 0, xy≤ -1}, and let C={a+b| a∈ A, b∈ B}. Then (A) {(x,y)∈ℝ²| x=0, y≥ 0} is a subset of C (B) {(x,y)∈ℝ²| x=0, y>0} is a subset of C (C) {(x,y)∈ℝ²| x≥ 0, y=0} is a subset of C (D) {(x,y)∈ℝ²| x>0, y=0} is a subset of C

Also written as: Let A={(x,y) in R^2| x>= 0, y>= 0, xy>= 1} and B={(x,y) in R^2| x<= 0, y>= 0, xy<= -1}, and let C={a+b| a in A, b in B}. Then

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 2017 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.