I was reviewing sets and Venn diagrams with my 8th grade math students last week as I was getting them ready for the round of state tests. Perhaps it’s a sign that I have been teaching this way too long, but my mind was wandering all over during the lesson. For some reason, the vocabulary and diagrams of set theory reminded me of marriage. Weird, I know. Well, I didn’t include this in my lesson (although maybe they would have been more interested?), but here is what I realized about the connection between three terms in set theory and how they relate to three styles of relationships.

# Union

In math, a union is when two or more sets are combined. In the Venn diagram above, the union of A and B is the entire shaded region. The symbol for union is a U. In a relationship that forms a union, each partner brings his or her whole self to the marriage and loses nothing when their lives overlap. The area in the center represents the deepening that occurs when two whole, healthy people unite. The shared region is the marriage, whereas the shaded regions that do not overlap represent the individuals and their independent beliefs and activities. The symbol for union, U, emphasizes that these relationships are open to outside influence and change. This would be the ideal relationship, each person contributing, benefiting, and yet remaining intact.

# Intersection

An intersection is the region where two or more sets overlap, shown by the center area in the Venn diagram above. It is represented by the symbol ∩. In a relationship characterized by the intersection model, each individual came to the marriage whole, but since has lost the part of him or herself that is not shared with the partner. This is a limited relationship as each person exists only in the overlap. The symbol for intersection demonstrates this closed, insular nature. These relationships may last, but you would be hard-pressed to find a happy partner in one.

# Subset

A subset is a set contained entirely within another set, shown with a symbol that looks like a C. In this type of relationship there is a power imbalance as one partner becomes completely absorbed by the other. The symbol represents the subset spouse being open only to his or her partner and not accepting any other influence. A relationship could start out in this fashion or this subset/superset could develop over time.

Which type of relationship best describes your marriage? Which type do you want to be? And could you pass the state algebra test now?

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I must say that this question was an intriguing challenge for me. I believe that our marriage is more like the first choice (Union Diagram) according to your description, “each partner brings his or her whole self to the marriage and loses nothing when their lives overlap.” However, this is a relationship that developed over time. There were times that I felt as if I had lost elements of myself. But I realized that I had actually put them aside because I thought that it was required. I am still learning that much of my self denial was self inflicted based upon my own presuppositions.

In fact the more that I consider the various diagrams, I might have related to each symbol in one period of time concerning our marriage.

Thank you for this post. DrMJ

I would guess that most relationships have or have had aspects of each diagram. I think it takes some wisdom, experience, and a letting go of fear to be able to fully embrace the union model.

I’m back, and your comment seems to fit best with what I feel about my relationship; that at different times, it might have been any of the diagrams, but not in a linear fashion, that they interchanged one another, depending on the time… This makes sense to me…

Le Clown

So little in life is linear…except in my algebra classroom, that is:)

Good. Now let’s be friends.

Le Clown

I will have to think about this one, but I think my wife and I are in the “Union” subset… I’ll be back with this one.

Le Clown

Maybe only during a “honeymoon” phase but couldn’t a complete union, where all values of each are equal, exist also? To have been young and in love at one time, all I saw in my partner was the reflection of my feeling toward her.

Then by the same token a non-union is possible (or maybe that is called divorce if left unresolved)? Over time many couples may grow apart for various reasons; most overcome it, some learn to live with it and others eventually divorce.

However, that is only an observation of my experience. I do think relationships 1)do not remain in one realm over time and 2)the heart of a successful one lays in the vows taken by each person (with or without a ceremony).