Find sets A, B and C such that \[A \cap B, A \cap C \text{ and } B \cap C\]are non-empty sets and\[A \cap B \cap C = \phi\]

Let us consider the following sets,A = {5, 6, 10 }B = {6,8,9}C = {9,10,11} \[\text{ Clearly }, A \cap B = \left\{ 6 \right\}\]\[B \cap C = \left\{ 9 \right\}, A \cap C = \left\{ 10 \right\} \text{ and } A \cap B \cap C = \phi\]\[\text{ It means that }, A \cap B, B \cap C \text{and}] A \cap C \text{ are non empty sets }\]\[\text{ and } A \cap B \cap C = \phi\]

P Find Sets A, B and C Such that a ∩ B , a ∩ C and B ∩ C Are Non-empty Sets and a ∩ B ∩ C = ϕ - Mathematics

Question

Find sets A, B and C such that $A \cap B, A \cap C and B \cap C$ are non-empty sets and $A \cap B \cap C = ϕ$

Solution

Let us consider the following sets,
A = {5, 6, 10 }
B = {6,8,9}
C = {9,10,11}

$Clearly, A \cap B = {6}$
$B \cap C = {9}, A \cap C = {10} and A \cap B \cap C = ϕ$
$It means that, A \cap B, B \cap C and] A \cap C are non empty sets$
$and A \cap B \cap C = ϕ$

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Types of Sets - Universal Set

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Q 8 Q 7.2 Q 9

Chapter 1: Sets - Exercise 1.06 [Page 27]

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Chapter 1 Sets
Exercise 1.06 | Q 8 | Page 27

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P Find Sets A, B and C Such that a ∩ B , a ∩ C and B ∩ C Are Non-empty Sets and a ∩ B ∩ C = ϕ - Mathematics

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