Step 1: List what Mendel is actually credited with.
Mendel worked with pea plants and from his results proposed the law of dominance, the law of segregation, and the law of independent assortment. For this body of work he is called the father of genetics.
Step 2: Check the timeline of the linkage idea.
The idea of linked genes, genes sitting close together on the same chromosome and being inherited together, was worked out later by Bateson and Punnett, and developed further by Morgan's group using fruit flies, decades after Mendel's original pea experiments.
Step 3: Note why Mendel could not have found linkage.
Mendel happened to study traits that assorted independently, so his own data did not show the linked inheritance pattern that would have revealed linkage even if it were present.
Step 4: Check the remaining statements.
Calling Mendel the father of genetics, saying he used pea plants, and saying he proposed the law of dominance are all accurate and match the historical record.
Final Answer:
The false statement is that Mendel discovered linkage, since that credit belongs to later scientists, option (3).