Step 1: Recall what FAP is.
Familial adenomatous polyposis (FAP) is an autosomal dominant disorder caused by a germline defect in the APC (adenomatous polyposis coli) gene, also called the FAP gene. Patients grow hundreds to thousands of colonic adenomatous polyps starting in the teenage years.
Step 2: Trace the molecular pathway.
The normal APC protein holds beta catenin down and stops it building up in the cell. When APC is defective, beta catenin escapes this control, moves into the nucleus, and pairs with the TCF transcription factor. This active complex switches on growth genes, including c-myc and cyclin D1.
Step 3: Work out the effect on c-myc.
Because the APC defect removes the brake on beta catenin signalling, c-myc gene expression goes up, not down. This raised c-myc output drives the unchecked proliferation of colonic epithelium that produces the numerous polyps.
Step 4: Check the remaining options.
FAP is indeed caused by a defect in the FAP (APC) gene, so that statement is true. The disease does show proliferation of colonic epithelium, so that is also true. Circulating antibodies to normal mucin have also been described in FAP patients as part of the altered mucosal response, so that statement is accepted as true too.
Final Answer:
Since c-myc expression is actually increased, not decreased, in FAP, the statement claiming decreased c-myc expression is the one that is NOT true.
\[ \boxed{\text{C-myc gene expression decreased}} \]