Final answer:
The true statement about the Battle of Gettysburg is that Lee invaded the North to dishearten the Union and alleviate pressure off Virginia. Other options provided are inaccurate, notably the Confederacy and Union did not lose half their men, and the battle's outcome was recognized as a setback for the Confederacy.
Step-by-step explanation:
The correct representation of what was true of the Battle of Gettysburg is an option (a): Lee decided to invade the North to dishearten the Union and take pressure off Virginia. General Robert E. Lee sought to carry the war into Union territory, aiming for a morale-damaging victory on Northern soil that might convince foreign powers to support the Confederacy and persuade the North to consider peace talks.
The statement that the Confederates and the Union each lost about half their men is inaccurate; although the battle resulted in extremely high casualties for both sides, the Confederacy suffered around 28,000 casualties, and the Union suffered approximately 23,000, which did not constitute half of their respective forces.
The assertions that Jefferson Davis viewed Gettysburg as a major victory, that Union forces under Meade pursued and lost Lee in the woods, and that Lee considered moving toward Washington but was convinced otherwise by his generals are all false. In reality, the defeat at Gettysburg was acknowledged as a significant setback for the Confederacy, Meade did not aggressively pursue Lee's retreat, and the Confederate army ultimately returned to Virginia without further attempts to engage the Union near Washington after Gettysburg.