Our reader’s question is: “There are two sets of symbols for ‘union’ and ‘intersection’. One is the ∪ and the upside down ∩, and the other set is the ∨ and the ∧. What is the relationship between these symbols, which we sometimes think of as ‘U’s and ‘V’s?”
So let’s mind our Us and Vs, and their upside-down companions, in unions and intersections as well as logical functions.
Symbols are everywhere in math, but do you know what they mean? Image by Mike DeHaan
The Math Symbols from the Question about Union and Intersection
The “V” symbols in the reader’s question are ∨ and ∧, which mean “Logical Or” and “Logical And.” The ∧ is a capital Greek Lambda.
The small ^ or “caret” is available on most keyboards as “shift-6″; it symbolizes the exponentiation function. It is important not to confuse ^ with ∧.
The symbol for “Union of sets” is ‘∪‘, while the symbol for “intersection of sets” is ‘∩.’
Set Theory for Union and Intersection
We use Venn Diagrams to show unions and intersection. Image by Mike DeHaan
The approach which relates most closely to the question involves set theory. Let A={a, e, i, o, u, y} and B={a, b, c, d, e, f}.
The union of sets ‘A’ and ‘B’ is the set containing the unique elements found in either set ‘A’ or set ‘B’, or both. In other words, “Bring all the elements together but discard duplicates”. A∪B={a, b, c, d, e, f, i, o, u, y}.
The intersection of sets ‘A’ and ‘B’ is the set containing the unique elements from both set ‘A’ and set ‘B’. In other words, to create an intersection, only select elements found in both original sets, which are the duplicates discarded by the union operation. A∩B={a, e}
With reference to the original question, from the view of set theory, the word “union” relates to the ‘∪‘ symbol; and the word “intersection” relates to the ‘∩’ symbol.
Click to Read Page Two: The Mathematical Logic of “And” and “Or”
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