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  • If A = {1, 2, 3} and B = {2, 3, 4}, what is the result of <div cl

If A = {1, 2, 3} and B = {2, 3, 4}, what is the result of {A\cup (A\cap B)}?

Option: 1

{1, 2, 3, 4}


Option: 2

{2, 3}


Option: 3

{1, 2, 3}


Option: 4

None of the above


Answers (1)

best_answer

First, we need to evaluate the intersection of sets A and B, which contains the elements that belong to both sets. 

In this case, the elements that belong to both sets A and B are 2 and 3.

 {(A\cap B)=\left\{2,3 \right\}}

Then, we need to evaluate the union of set A and the intersection of sets A and B, which contains all the elements that belong to either set A or the intersection of sets A and B. 

In this case, the elements that belong to set A are 1, 2, and 3, and the elements that belong to the intersection of sets A and B are 2 and 3.

\Rightarrow {A\cup (A\cap B)=\left\{ 1,2,3 \right\}\cup \left\{ 2,3 \right\}}

\Rightarrow {A\cup (A\cap B)=\left\{ 1,2,3 \right\}}

Therefore, the result of   {A\cup (A\cap B)} is {1, 2, 3}.

 

Posted by

sudhir.kumar

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