Prepare the artichokes for cooking. Slice the stems off, leaving about 1/2-inch, and remove the lower leaves. Slice about 1/2- to 1-inch off the top of each artichoke, then use kitchen scissors to snip the tips of each outer leave. If desired, rub lemon juice over cut surfaces to prevent browning.
Fill the Instant Pot with 1.5 cups water. This is the recommendation for a 6 quart Instant Pot. If you have an 8 quart Instant Pot, you will need to increase the water to 2.5 cups. Place the trivet in the Instant Pot, and put the artichokes upside down on the trivet. Seal the lid on the Instant Pot, and set the cook time for 20 minutes. It will take a few minutes to come to pressure.
When the artichokes are finished cooking, turn the valve on the lid to manually release the pressure. Be careful when doing this; wear an oven mitt and step away from the steam. Once the Instant Pot is finished releasing pressure, remove the lid. The artichokes are ready if a fork can easily be inserted into the stem and the leaves can be easily pulled off. Use tongs to take the artichokes out. You can also let them sit in the Instant Pot with the lid closed for a few minutes after the pressure releases. This will make them even softer.
Serve the artichokes with dipping sauce of choice. Eat the artichokes by removing a leaf and scraping the inside leaf along your teeth. Discard the outer leaves after eating, but you may be able to eat some of the inner leaves whole if they are very soft. Avoid eating the fuzzy choke in the center! You can, however, eat the artichoke heart. I prefer to slice the cooked artichokes in half and remove the choke before eating, but it's up to you.