Is it true that in the battle of Fair Oaks neither side won a victory?

Yes, it is true that in the Battle of Fair Oaks, fought from May 31 to June 1, 1862, neither the Union nor the Confederate forces achieved a decisive victory. The battle resulted in heavy casualties for both sides and effectively ended in a stalemate, with both armies holding their positions. Although the Union Army maintained control over the battlefield, they did not gain a strategic advantage that could be considered a clear victory over the Confederates.