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ACSEE (Form 6) Sets — practice questions

Explore 8 free Sets questions in ACSEE (Form 6) Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Sets questions and exercises with answers

Showing questions 1–8 of 8.

Using the laws of algebra of sets, $(A\cap B')\cup(A'\cup B')$ simplifies to:Read the answer and worked solution →Using the laws of algebra of sets, $(A\cup B)'\cap(A\cap B)'$ simplifies to:Read the answer and worked solution →Place the survey studentsRead the answer and worked solution →Name the law of setsRead the answer and worked solution →A class list $A$ has the pupils who play football removed, leaving set $B$ behind. The remainder $A-B$ equals:Read the answer and worked solution →If $B=\{x:2\le x\le5\}$, then its complement $B'$ is:Read the answer and worked solution →Sort the set regionsRead the answer and worked solution →Complete the set lawsRead the answer and worked solution →

Worked practice questions

Using the laws of algebra of sets, $(A\cap B')\cup(A'\cup B')$ simplifies to:

  1. $B'$
  2. $A'\cap B'$
  3. $A\cap B'$
  4. $A'\cup B'$
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Correct answer: D. $A'\cup B'$

1. Note $A'\cup B'$ already contains every element outside $A$ or outside $B$. 2. The set $A\cap B'$ consists of elements in $A$ but not in $B$, so each of them lies in $B'$ and therefore in $A'\cup B'$. 3. A union with one of its own subsets changes nothing: $(A\cap B')\cup(A'\cup B')=A'\cup B'$. 4. Collapsing the answer to $B'$ discards the $A'$ part of the union. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 5: Sets_

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Using the laws of algebra of sets, $(A\cup B)'\cap(A\cap B)'$ simplifies to:

  1. $A'\cap B'$
  2. $A\cup B'$
  3. $A'\cup B'$
  4. $B$
Show answer and solution

Correct answer: A. $A'\cap B'$

1. By De Morgan's law $(A\cup B)'=A'\cap B'$ and $(A\cap B)'=A'\cup B'$. 2. The expression becomes $(A'\cap B')\cap(A'\cup B')$. 3. Here $A'\cap B'$ is a subset of $A'\cup B'$, so the intersection returns the smaller set. 4. Hence the result is $A'\cap B'$. 5. Answering $B$ applies De Morgan's law to only one bracket and then cancels wrongly. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 5: Sets_

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Place the survey students

Read exercise and reference answers
Left
Economics
Items
  1. Region
    Economics
    Item
    Econ only: 82
  2. Region
    Economics
    Item
    Econ total: 329
  3. Region
    Geography
    Item
    Geog only: 40
  4. Region
    Geography
    Item
    Geog total: 186
  5. Region
    both
    Item
    Both E and G: 83
  6. Region
    both
    Item
    All three: 53
Right
Geography
Instructions
Tap an item, then the region of the diagram it belongs to.

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