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The molecular formula of the first member of alkenynes and its name is given by the set:
$A.\;{C_3}{H_2}$, Alkene
$B.\;{C_5}{H_6}$, Pent-1-en-3-yne
$C.\;{C_6}{H_8}$, Hex-1-en-5-yne
$D.\;{C_4}{H_4}$, But-1-en-3-yne

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Hint: Alkynes is a hydrocarbon, in which a triple bond binds two carbon atoms. The simplest alkyne would therefore have 2 carbon atoms within its molecule.
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First member of Alkenynes

Complete answer:
The general formula for alkynes is ${C_n}{H_{2n - 2}}$ where C is the Carbon atom and H is Hydrogen atom and n = 2,3,4,5.......
We will call the structure as meth, eth, prop, but, pent, hex, hept, oct, non, dec etc according to the number of carbon atoms present.
Usually we don't use meth as the simplest Alkyne has 2 carbon atoms and meth is used for 1 carbon atom, so we can use eth directly
For example, when we substitute the value of n = 2 in the formula ${C_n}{H_{2n - 2}}$, we get ${C_2}{H_2}$
To nomenclature this compound we will apply 'yne' to the number of carbon atoms used as the primary suffix. And here we used 2 carbon atoms, the name of the compound will be :- Eth + yne = Ethyne
${C_4}{H_4}$ will be the first member of the alkenyes group and no other compound can be smaller than this compound.

Hence, option D is the correct answer, which is ${C_4}{H_4}$, But-1-en-3-yne is the first member of alkenynes.

Note: While solving such types of problems we must remember the properties of Carbon atoms and the properties of alkenynes. In this alkenynes is given by ${C_n}{H_{2n - 2}}$ and the smallest compound that can exist is ${C_4}{H_4}$, But-1-en-3-yne. Also, we must know how to do the naming of the compound.