The correct answer is E: I, IV, and V.
Here's a quick breakdown:
I. The election was indeed settled by Congress due to the disputed results. II. Rutherford B. Hayes did not soundly defeat Samuel J. Tilden; the election was very close. III. This statement is incorrect; Tilden did not defeat Hayes in the Electoral College. IV. Hayes defeated Tilden in the Electoral College, which is correct. V. The disputed 20 electoral votes were awarded to Hayes on the agreement that federal troops would be withdrawn from the South, which is also correct.
Therefore, I, IV, and V are accurate statements about the election of 1876.