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The correct IUPAC name of the compound $ HOOC - C{H_2} - C{H_2} - COOH $ is:

Answer
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Hint: For naming an organic compound in accordance with IUPAC rules, we should keep in mind the basics which include the number of Carbon atoms in the compound, the substituents present if any, the types of functional groups present and their positions. This will help us name any organic compound easily.

Complete answer:
IUPAC or International Union of Pure and Applied Chemistry, has set down a particular set of rules to be followed which are universally accepted while naming organic compounds. The IUPAC naming, is a standardized naming system for the compounds, while there exist general and trivial names for compounds.
The given organic compound is as follows:
 $ HOOC - C{H_2} - C{H_2} - COOH $
This compound has four Carbon atoms in total in a single carbon chain. The chain has no substituents. The functional group present is Carboxylic acid $ \left( { - COOH} \right) $ . There are two carboxylic acid groups in the compound at both terminals.
The alkane having four carbon atoms is called butane $ \left( {C{H_3} - C{H_2} - C{H_2} - C{H_3}} \right). $ There are two carboxylic acid groups present in the organic compound, which is called “dioic” as the carboxylic acids have the suffix “oic”. Hence, the IUPAC name of the compound is Butanedioic acid.

Note:
The position of the carboxylic groups is not specified using numbers in the IUPAC name of the compound. This is because on this chain $ - C{H_2} - C{H_2} - $ two carboxylic acid groups can only attach in a single manner. The compound if numbered from both sides and named will give the same name eventually and hence this is ignored.