Fallacy of division

The fallacy of division, also know as false division arises when the inference of an argument depends on the erroneous transference of an attribute of the whole to the parts. This is the exact reverse of the fallacy of composition.

Examples

 * "His church is about half the size of most churches in the city, therefore, the pastor of this church should be about 3 feet tall"
 * Christian churches do not teach science, therefore creationists are uneducated about science.

Formal example
Formally speaking this fallacy has the following structure:


 * p is part of w
 * w has property t
 * therefore, p has property t