I find the Punnett square useful for things beyond classroom biology. Let's pick the words "forgive" and "forget", and set up a 2x2 square:
Legend:
A = YES Forgive, YES Forget
B = NO Forgive, YES Forget
C = YES Forgive, NO Forget
D = NO Forgive, NO Forget
"To Forgive and Forget" is an old, precariously wise sentiment. It means what it says with no caveats.
Excerpt from: [Does the Bible say Forgive and Forget?]
Most likely, it is Miguel de Cervantes (1547-1616) who said forgive and forget. The phrase comes from his 17th Century book "Don Quixote." The proper quote is "Let us forget and forgive injuries."
Around the same era, William Shakespeare (1564-1616) used the phrase in "King Lear": "Pray you now, forget and forgive". Shakespeare links prayer to forgiving and forgetting, which sounds more related to the message in the Bible.
"To Forget but Not Forgive" is a habit of dull minds, or at least short memories, and is as common as air. Nearly everyone does this proudly, all with help from Maya Angelou:
I've learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel.
This kind of stuff ends up on living room walls, stitched into pillows, etched on candles, it goes on forever. While the quote has some insight, try to explain how this isn't the epitome of forgetting while not forgiving.
"To Forgive but Not Forget" is an extremely useful case. This is what happens when your 14 year old nephew drives the car through the garage door accidentally. Sure, you will forgive this incident after it's decided who pays for the damage. The damage though, is never forgotten.
"To Not Forgive and Not Forget" is what it means to hold a grudge. This is a clinging resentment to a past offense or injury. It's not even a bad thing.