Why were the siege of vicksburg and the battle of gettysburg crucial to the outcome of the war?

The Siege of Vicksburg was important to the Union troops because they were able to take control of the Mississippi River. This allowed the Union troops to cut the Confederacy in half and allowed the Union to cut of supplies/resources to Confederate states.

The Battle of Gettysburg was an important Union win because this was the last time in the Civil War that the Confederate troops truly invaded the North. After this battle they did not invade any state north of Pennsylvania.

False but idk if im right