Answer :

rvkacademic

Answer:

1)  A ∪ B =  {0, 1, 2, 3, 4, 5 ,6 ,9}

2)  A ∩ C = {0, 2}

3) A ∪ B ∪ C  = {0, 1, 2, 3, 4, 5, 6 7. 8. 9}

4)  A ∩ B ∩ C = {0}

Step-by-step explanation:

Definitions

Union of two or more sets is the set of elements in all of those sets with duplicates removed. The symbol used is ∪

Intersection of two or more sets is the set of elements common to those sets. Symbol ∩

1) A ∪ B = {0, 1, 2, 3, 4, 5} ∪  {0, 1, 5, 6, 9}  = {0, 1, 2, 3, 4, 5 ,6 ,9}

2) A ∩ C =  {0, 1, 2, 3, 4, 5} ∩  {0, 2, 6, 7, 8} = {0, 2}

3) A ∪ B U C = (AUB) ∪ C

=  {0, 1, 2, 3, 4, 5 ,6 ,9} U  {0, 2, 6, 7, 8} = {0, 1, 2, 3, 4, 5, 6 7. 8. 9}

4)  A ∩ B ∩ C​ =   {0, 1, 2, 3, 4, 5}   ∩   {0, 1, 5, 6, 9} ∩     {0, 2, 6, 7, 8}

= {0}

semsee45

Answer:

1) A ∪ B = {0, 1, 2, 3, 4, 5, 6, 9}

2) A ∩ C = {0, 2}

3) A ∪ B ∪ C = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

4) A ∩ B ∩ C​ = {0}

Step-by-step explanation:

Set Notation

[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]

Given sets:

  • A = {0, 1, 2, 3, 4, 5}
  • B = {0, 1, 5, 6, 9}
  • C = {0, 2, 6, 7, 8}

Question 1

[tex]\begin{aligned}\sf A \cup B & =\sf \{ 0, 1, 2, 3, 4, 5 \} \cup \{0, 1, 5, 6, 9 \}\\& =\sf \{ 0, 1, 2, 3, 4, 5, 6, 9 \}\end{aligned}[/tex]

Question 2

[tex]\begin{aligned}\sf A \cap C& =\sf \{0, 1, 2, 3, 4, 5 \} \cap \{ 0, 2, 6, 7, 8 \}\\& =\sf \{0, 2 \}\end{aligned}[/tex]

Question 3

[tex]\begin{aligned}\sf A \cup B \cup C& =\sf \{ 0, 1, 2, 3, 4, 5 \} \cup \{0, 1, 5, 6, 9 \} \cup \{0, 2, 6, 7, 8 \}\\& =\sf \{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 \}\end{aligned}[/tex]

Question 4

[tex]\begin{aligned}\sf A \cap B \cap C& =\sf \left(A \cap B\right) \cap \left(B \cap C\right) \\ & =\sf \left(\{ 0, 1, 2, 3, 4, 5 \} \cap \{0, 1, 5, 6, 9 \}\right) \cap \left(\{0, 1, 5, 6, 9 \} \cap \{0, 2, 6, 7, 8 \} \right)\\& =\sf \{ 0, 1, 5 \} \cap \{0, 6 \}\\ & = \sf \{ 0 \}\end{aligned}[/tex]

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