Math notation for testing whether a number is less than two numbers

Question

Given numbers $a$, $b$ and $c$ what's the correct math notation for testing whether $a$ is less than or equal to $b$ and $c$.

1) $$a \leq b \land a \leq c$$

2) $$a \leq b \land c$$

3) $$a \leq \{b, c\}$$

4) $$a \leq (b, c)$$

Answer 1

I would write it just as $a\leq b, c$. It's common enough when you, for instance, want to multiply all different pairs of elements from some indexed collection $\{a_0, a_1, \ldots, a_n\}$ to use $a_i\cdot a_j$ for $0\leq i, j\leq n$, meaning exactly that $0\leq i\leq n$ and $0\leq j\leq n$.

If you want to get technically strict, then any of the following will do: $$a\leq b \land a\leq c\\ a\leq b \text{ and }a\leq c\\ a\leq \min(b, c)$$ Of these I prefer the middle one, because to me it is the easiest one to read and immediately understand.

Answer 2

1) is correct if $\wedge$ means "and". Of course it is better to just write "and".

2) is correct if $\wedge$ means "minimum". But of course do not just write it without explanation.

Probably 3) could be correct, with the right interpretations.

I think 4) is wrong in any interpretation I can think of.

Since you say this is part of an algorithm, the answer will be determined by what $\wedge$ was defined to be in that course or book.