It is logical to conclude that water cannot dissolve vegetable oil because the oil is

In chemistry, there is a common note that says, "Like dissolves like".

This pertains to the concept that polar substances can dissolve only other polar substances. Also, nonpolar substances are also only able to dissolve nonpolar substances.

Polarity of the substance depends primarily on the type of bond and the difference in electronegativity.

Water is a polar substance while vegetable oil is not. From the concept presented above, it may be concluded that water will not be able to dissolve the vegetable oil and the assumption is logical.