What is a term for two events where the absense of one assures the absense of the other? With two events, there are three types of what i've dubbed 'mutual patterns':

Mutual Inclusion

A    B
1 -&gt; 1 If A then B
1 &lt;- 1 If B then A

A &lt;-&gt; B 


Mutual Exclusion

A    B
1 -&gt; 0 If A then NOT B
0 &lt;- 1 If B then NOT A

NOT A &lt;-&gt; B
NOT B &lt;-&gt; A


Mutual erm...   ¯\_(ツ)_/¯

A    B
0 -&gt; 0 If NOT A then NOT B
0 &lt;- 0 If NOT B then NOT A

NOT A &lt;-&gt; NOT B


See, here's where the confusion lies. For 2 of the three patterns, you have words used to describe those two patterns which are antonyms to each other. I.e their opposites. So there is no third term beyond exclusion and inclusion, but the type of pattern where the absence of A assures the absence of the other B and vice versa, still shares this notion of mutuality. In other words, it's like am looking for a third opposite... Which I don't think is possible.
The statement:
$$
(\textrm{Not} \ A) \Leftrightarrow (\textrm{Not} \ B)
$$
is equivalent to the statement:
$$
 A \Leftrightarrow  B 
$$
P.S.: You can easily check that the above statements are contrapositives.
I'm not sure I understand this question.

That said, we might write:

1. A is absent of truth, B is absent of truth.
2. A is absent of truth, B is present with truth.
3. A is present with truth, B is absent of truth.
4. A is present with truth, B is present with truth.


Here, the cases where the absence of one proposition assures the absence of the other are cases 1. and case 4.  This accords with the truth table for exclusive disjunction.