Draw the condensed structural formulas for two different molecules with the formula \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}\) .

First, we will draw three different structural formulas that comply with the given molecular formula \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}\). Option 1: \(\mathrm{H}_{2} \mathrm{C}= \mathrm{C}- \mathrm{CH}_{2} \mathrm{O}\) Option 2: \(\mathrm{H}_{2} \mathrm{C}= \mathrm{C}- \mathrm{C}(\mathrm{OH})_{2}\) Option 3: \(\mathrm{HC}\equiv \mathrm{C}- \mathrm{CH}_{2} \mathrm{OH}\)

Now, let's determine if all these structures are valid based on the bonding rules for each atom (C can form four bonds, H forms one bond, and O forms two bonds). Option 1: \(\mathrm{H}_{2} \mathrm{C}= \mathrm{C}- \mathrm{CH}_{2} \mathrm{O}\) In this structure, each carbon atom forms four bonds, the hydrogen atoms form one bond each, and the oxygen atom forms two bonds. Thus, this structure is valid. Option 2: \(\mathrm{H}_{2} \mathrm{C}= \mathrm{C}- \mathrm{C}(\mathrm{OH})_{2}\) In this structure, each carbon and hydrogen atom forms the correct number of bonds, but the oxygen atoms violate the rule since they form only one bond each. Thus, this structure is not valid. Option 3: \(\mathrm{HC}\equiv \mathrm{C}- \mathrm{CH}_{2} \mathrm{OH}\) In this structure, each carbon atom forms four bonds, the hydrogen atoms form one bond each, and the oxygen atom forms two bonds. Thus, this structure is valid.

Now that we have identified the two valid structures, we can draw their condensed structural formulas. Option 1: \(\mathrm{H}_{2} \mathrm{C}= \mathrm{C}- \mathrm{CH}_{2} \mathrm{O}\) Condensed formula: CH\(_2\)=CHOCH\(_2\) Option 3: \(\mathrm{HC}\equiv \mathrm{C}- \mathrm{CH}_{2} \mathrm{OH}\) Condensed formula: HC≡CCH\(_2\)OH These are the condensed structural formulas for two different molecules with the formula \(\mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}\).