characterized by rigor; rigidly severe or harsh, as people, rules, or discipline

rigorous laws.

severely exact or accurate; precise

rigorous research.

(of weather or climate) uncomfortably severe or harsh; extremely inclement.

Logic, Mathematics . logically valid.

adjective

easy , easy-going , lax , lenient , loose , mild

adjective

accurate , ascetic , austere , bitter , brutal , burdensome , correct , definite , dogmatic , exacting , hard , harsh , inclement , inflexible , intemperate , ironhanded , meticulous , nice , onerous , oppressive , precise , proper , punctilious , right , rigid , rugged , scrupulous , stern , stiff , strict , stringent , uncompromising , unpermissivenotes:rigorous means demanding strict attention to rules and procedures; vigorous means strong and active physically or mentally , exact , arduous , backbreaking , demanding , difficult , effortful , exigent , formidable , heavy , laborious , rough , severe , taxing , tough , trying , weighty , faithful , full , errorless , true , veracious , veridical , challenging , relentless , unyielding