Designing "and", "or" Icons

Question

I am trying to come up with a good design for a pair of icons that will be placed above a list of tags which filter a list of items.

Basically the tags that are ticked can search using "and" or using "or" so you can find all items that have "tagA OR tagB" or you can search for all items with "tagA AND tagB".

              [] []        <------ Icons
|---------|  |----------|
|Items:   |  |Tags:     |
| - Item1 |  | [] TagA  |
| - Item2 |  | [] TagB  |
| - Item3 |  | [] TagC  |
| - Item4 |  |----------|
| - Item5 |
|---------|

I have a few ideas of how to represent this but nothing that I am happy with.

I have a 16x16 area to fit each icon into.

So if anyone has any ideas on a pair icons that would work to convey this idea then I'd be very happy to hear them.

Answer 1

For "and" you could obviously use & or + -- these would be the most intuitive.

For "or" something which indicates a "split" might work....

Just need to be careful it doesn't look like "less than"

Answer 2

There is a symbol for it in predicate logic.

"And/or" is just called "or" and is represented as ∨, from the Latin vel meaning or. But note that it's a separate symbol from the letter "v", though similar.

In contrast, "or" in the sense of "this one or that one but never both" is called "exclusive or" or "xor" and can be symbolized as ⊻ or ⊕.

Also, in programming you might see "and/or" represented as | or as ||, and "xor" represented as ^. Which confusingly looks a lot like ∧, used in logic to mean "and".

I take "ZERO" credit for research or this explanation Henrik N --> Source - english.stackexchange.com/

I know this is about 'and/or' but the symbols expressed above are used for 'or' in mathematics and programing. Although no overly helpful; BUT hopefully this will give you or someone else some ideas.