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Find the intersection of $A$ and $B$, and represent it by Venn diagram: $A = \{ 1,2,4,5\} ,B = \{ 2,5,7,9\} $

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Last updated date: 18th Jun 2024
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Answer
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Hint: Look for elements which are common to the sets A and B. The set of these elements is the correct answer. Then draw the Venn diagram.

Complete step by step solution:
We are given two sets $A = \{ 1,2,4,5\} $ and $B = \{ 2,5,7,9\} $.
We are asked to find the intersection of $A$ and $B$.
We know that the intersection of any two non-empty sets is a set containing the elements belonging to both the non-empty sets. Also, the intersection of two sets $A$ and $B$ is denoted by $A \cap B$.
Now, the elements of $A$ are 1, 2, 4, and 5 and the elements of B are 2, 5, 7, and 9.
Therefore, $A \cap B = \{ 2,5\} $
For representation by Venn diagram, we draw one circle each for $A$ and $B$ as follows:
seo images

Here the shaded part represents $A \cap B$.

Note: When there are no elements common between the two sets $A$ and $B$, their intersection is an empty set $\emptyset $ (read as phi) and we write it as $A \cap B = \emptyset $.