(a) By the process of elimination.
--Sarah Hanson's husband, Joseph Stroup, is buried in South Solon Cemetery, b. 14 Aug. 1816, d. 8 Nov. 1894.
--Madison Co. John and Mary Stroup had "five sons and two daughters."Their sons were:William, John, David, Joseph, and Jacob.John and Mary deed four hundred acres to the last four in 1824 (I think).William was a witness to the deed.
--There are three Joseph Stroups in Madison Co. in 1850:Joseph Sr., son of John and Mary and husband of Jane Denton, whom he married in 1827 in Madison Co.;Joseph Jr., son of Joseph Sr. and Jane (nee Denton) Stroup; and Joseph, husband of Sarah A. (nee Hanson) whom he married in 1846 in Madison Co.
--Sarah Hanson's Joseph was neither son of John and Mary Stroup nor son of Joseph Sr. and Jane (nee Denton) Stroup.
--John and Mary's son, David, married Mary Ray in 1822 in Madiosn Co. and I am informed that his children are well documented and do not include Sarah Hanson's Joseph.
--Sarah Hanson's Joseph was born in 1816 and John and Mary's son, Jacob, was born in 1802.It would be a far stretch of my imagination to think that Sarah Hanson's Joseph was son of Jacob.
--John and Mary's son, John Jr., died 18 Jan 1845.I have no marriage date for him.However, I notice that John Jr. is not a head of a household in the 1820 or 1830 census.I note that there is 1 male in John and Mary's 1830 household who is 30 and under 40 years old, who I believe is their son, John, in which case he was not married by 1830.
Encouraging my belief that Sarah Hanson's Joseph was son of William and Ann (nee Thomas) Stroup is the assertion, in the biographical sketch of Reuben Stroup in The Biographical and Genealogical History of Cass, Miami, Howard, and Tipton Counties, Indiana (Lewis Pub. Co., 1898), pages 526-528, according to which:
"His father, William Stroup, was a native of Pennsylvania and of German descent, and was married in Ohio to Miss Anna Thomas, a native of Maryland. William was a son of John Stroup, a native of Germany, who settled in Pennsylvania. William emigrated to Ohio, when a young man, during the middle of the last century, and served seven years in the Revolutionary war, in which he received a wound, and finally died in Pennsylvania. William Stroup emigrated to Ohio when a young man, married there, and followed agricultural pursuits. In 1849 he sold his farm and came to Tipton county, Indiana, where he entered a tract of land, which is the present homestead of the family, and of this tract he made a good farm, being successful in its management. He died in 1863 at the age of seventy-eight years, well known among the pioneers of his section of the state as an honorable man and useful citizen. Politically he was a Democrat. His wife died in 1868, at the age of seventy years. They had ten children. John, deceased; Joseph, who died in Ohio; Polly, Jane, Rebecca, Anna, Naomi, Lavina, Reuben (our subject), and Jackson, a farmer."
Reuben Stroup's brother, Joseph, was a son of William and Ann (nee Thomas) Stroup and died in Ohio before 1898.Sarah Hanson's Joseph Stroup died in Ohio in 1894.