Both Uses

irrelevant
in
Tunnel In the Sky
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He felt that he knew what "Deacon" Matson would say ....something about the irrelevancy of fairness to survival.†
Chpt 1 *

irrelevancy = the state of not being relevant (not related to the subject being considered, or not important enough to want to consider)
"I just can't see," Rod answered irrelevantly, "how I could be so wrong.†
Chpt 5

irrelevantly = in a manner that is not relevant (not related to the subject being considered, or not important enough to want to consider)

Definitions:

(1) (irrelevant)
not relevant (not related to the subject being considered, or not important enough to want to consider)
(2) (meaning too rare to warrant focus)