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If we are given the sets $A=\left\{ 3,5,7,9,11 \right\},B=\left\{ 7,9,11,13 \right\},C=\left\{ 11,13,15 \right\}$ and $D=\left\{ 15,17 \right\}$, find $A\cap C$.

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: For solving this question you should know about the intersection and unions of two sets. These problems are solved by the formulas of intersection of more or two sets and union of two or more sets. We will just use the formulas for this and will directly solve this question very easily.

Complete step-by-step solution:
According to our question it is asked of us to find the value of intersection of two sets and we will find that by the help of simple formulas. As we know that if any two or more sets are given to us and asked to find the intersection of any two sets or more than two sets, then we will find the common number or common digits which are available there unless that is zero. And if that is asking for the union of two or more than two sets, then we will find all numbers which are available in all the sets. We will not repeat any number and will not leave any number. It means every number will appear only once.
If $A=\left\{ 3,5,7,9,11 \right\},B=\left\{ 7,9,11,13 \right\},C=\left\{ 11,13,15 \right\}$ and $D=\left\{ 15,17 \right\}$, then we have to find the following:
$A\cap C$
Here we have to find the intersection of sets A and C which means the common elements which are present in both sets. If we see closely to the given sets A and C we have only 11 as common elements. Hence,
$A\cap C=\left\{ 3,5,7,9,11 \right\}\cap \left\{ 11,13,15 \right\}=\left\{ 11 \right\}$
So, the answer is $\left\{ 11 \right\}$.

Note: While solving these type of questions you have to keep in mind that if it is asked for intersection, then we will consider only the common digits and if it is asked for the union, then we will write all the digits without repeating any digit. SO, we will find the intersection and union of the sets this way.