Question

read the diagram and answer the question given bellow find AuB,AnB,A-B,B-A,A'uB'​

Answer 1

Given :

• We are given a diagram with some elements.

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To find :

• $\sf\:A \cup B$

• $\sf\:A \cap B$

• $\sf\:A - B$

• $\sf\:B - A$

• $\sf\:A' \cup B'$

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Solution :

Calculating $\sf\:A \cup B$ -

➻ $\sf\:A \cup B$ means all the elements belonging to both A and B.

Elements in A = { 1,5,6,7,8 }

Elements in B = { 10,11,12,7,8 }

Their union -

$\sf\color{orange}{\:A \cup B = \left\{ 1,5,6,7,8,10,11,12 \right\}}$ $\sf\:⋆$

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Calculating $\sf\:A \cap B$ -

➻ $\sf\:A \cap B$ means only those elements which are common to both A and B.

Elements in A = { 1,5,6,7,8 }

Elements in B = { 10,11,12,7,8 }

Their intersection -

$\sf\color{orange}{\:A \cap B = \left\{ 7,8 \right\}}$ $\sf\:⋆$

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Calculating $\sf\:A - B$ -

➻ $\sf\:A - B$ means all those element belonging to A but not in B.

Elements in A = { 1,5,6,7,8 }

Elements in B = { 10,11,12,7,8 }

Therefore $\sf\:A - B$ -

$\sf\color{orange}{\:A - B = \left\{ 1,5,6 \right\}}$ $\sf\:⋆$

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Calculating $\sf\:B - A$ -

➻ $\sf\:B - A$ means all those element belonging to B but not in A.

Elements in A = { 1,5,6,7,8 }

Elements in B = { 10,11,12,7,8 }

Therefore $\sf\:B - A$ -

$\sf\color{orange}{\:B - A = \left\{ 10,11,12 \right\}}$ $\sf\:⋆$

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Calculating $\sf\:A' \cup B'$ -

➻ $\sf\:A' \cup B'$ means all those elements which belongs to Universal set but neither belongs to A nor to B.

Elements in A = { 1,5,6,7,8 }

Elements in B = { 10,11,12,7,8 }

Universal set = { 1,2,3,4,5,6,7,8,9,10,11,12,13 }

Therefore $\sf\:A' \cap B'$ -

$\sf\color{orange}{\:A' \cap B' = \left\{ 2,3,4,9,13 \right\}}$ $\sf\:⋆$

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More to know -

• A ⋂ B = A intersection B

• A ⋃ B = A union B

• A ⊆ B = A is a subset of B , set A is included in set B

• A ⊂ B = A is a subset of B , but A is not equal to B

• A ⊄ B = Set A is not a subset of B

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