Intersection of conditions

Question

If I have a list of conditions:

{cond1,cond2,cond3}

and I want to use an If[] statement to test the intersection of these conditions (or, more generally, any subset of them, but let's start with the basic case first):

If[cond1&&cond2&&cond3,a,b]

How would I do that?

Answer 1

Don't worry about whether these are trivial questions: they are good opportunities to explain a little more about Mathematica's syntax.

The first point is that what you already had works fine. You can confirm this using FullForm.

If[cond1 && cond2 && cond3, a, b] // FullForm
(*If[And[cond1,cond2,cond3],a,b]*)

If you preferred, you could type out the And construction explicitly.

J.M.'s comment invokes the Apply function to change the Head of a List of things, in this case the conditions, to And.

And @@ {cond1, cond2, cond3} // FullForm
(* And[cond1,cond2,cond3] *)

Or equivalently

FullForm[Apply[And, {cond1, cond2, cond3}]]
(* And[cond1,cond2,cond3] *)

The FullForm is just for explication; you wouldn't use it in normal operations. So the short syntax for the above is:

And @@ {cond1, cond2, cond3}
(* cond1&&cond2&&cond3 *)

The usefulness of storing your list of conditions as a list is that it is then easier to use various other list-manipulation techniques to get those subsets of conditions mentioned in your question.

And @@ (Most@{cond1, cond2, cond3})
(* cond1&&cond2 *)