I have variables a, b, and c. I would like to write the following sentence in my thesis:
There are possible sets of boolean values to test these variables such as a=true, b=false, c=true or a=false, b=true, c=false.
Is it correct if I write the sets as <a=true, b=false, c=true> and <a=false, b=true, c=false>? If the symbol < > is not correct, what is the correct one to use?
On
A triplet of variables is written $(a,b,c)$.
The set of possible values for each variable is written $\{\text{false},\text{true}\}$.
For one variable you can write $a\in\{\text{false},\text{true}\}$ to say that $a$ is either false or true.
To say you want a particular instance of three variables $a,b,c$ at the same time you can write: $$\text{for some }(a,b,c)\in\{\text{false},\text{true}\}^3$$
You can also use quantifiers $\exists$ or $\forall$ in place of the text "for some" if you want to consider existence or all possible triplets.
A particular instance can then be $(\text{true},\text{false},\text{true})$, you don't need to indicate that the first true is $a$ and so on, this is implicit from the order in the triplet, provided you specified earlier that the triplet was named $(a,b,c)$.
A similar statement than $a=\text{true}$ for a single variable would be $(a,b,c)=(\text{false},\text{false},\text{true})$ for a triplet.
Notation is really just conventional, so you can do whatever you want so long as you are clear.
IMO, I think the clearest thing would be e.g. "The possible values of $(a,b,c)$ include (true, false, true) and (false, true, false)."