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What distinctions can be made among the meanings of the words "inverse", "reverse", "converse", and, for good measure, "transverse" and "obverse"? Is it ever possible to use some of them interchangeably?
Are they the same for purposes of casual discourse? Do the differences become more salient in a particular technical context, such as engineering, math, or linguistics?
inverse: opposite or contrary in position, direction, order, or effect
in mathematics - something obtained by inversion or something that can be applied to an element to produce its identity element
reverse: opposite primarily in direction
in law - reverse or annul
in printing - make print white in a block of solid color or half tone
in electronics - in the direction that does not allow significant current
in geology - denoting a fault or faulting in which a relative downward movement occurred in the strata situated on the underside of the fault plane
converse: corresponding yet opposing
in mathematics - a theorem whose hypothesis and conclusion are the conclusion and hypothesis of another
also a brand of shoe
transverse: situated across from something
obverse: the opposite or counterpart of something (particularly a truth)
in biology - narrower at the base or point of attachment than at the apex or top
from NOAD
Reverse is the only one I've commonly heard in casual speech and only referring to the direction of a car (in US... don't know about UK et al). Some could be used interchangeably, but it would be best to avoid it considering that each generally has a specific meaning in its context.
obverse: the front side of a coin (as opposed to the reverse)
converse and inverse in mathematical logic take a conditional hypothesis and swap or negate its clauses, respectively:
The truth or falsehood of the original hypothesis is not equivalent to either the converse or the inverse, but the converse and the inverse are equivalent to each other.
These are good definitions and clarifications, but since I don't see direct answers, I will offer one. As a software engineer, I am familiar with logic, and so converse and inverse are everyday words for me.
The converse, defined as swapping hypothesis and conclusion, is of course a position change. Since reverse indicates direction, I have often heard and even used reverse as a natural substitute for converse.
Think of someone saying, "If I have to do it, you do too!" A common reply would be "And the reverse!" This is actually referring to the converse, but that would not be said by most people with whom I am familiar.
I believe that those are the only two that would be confused in casual discourse, and that the differences would indeed become more salient in technical contexts.
Don't forget the contrapositive, which goes from 'If I get $100, I shall buy a coat.' 'If I have not bought a coat, I have not received $100.'and is true when the original assertion were.
If A --> B (condition 'A' always implies condition 'B')
Converse:
B --> A
False---more than one road can lead to Rome (one might not have got the $100 but instead opted for cheaper pants)
Inverse: (for the 'not' operator '~')
~A --> ~B
False, for the same reason as is the Converse. (Remember,'A-->B' doesn't mean that A were the only way to get to B.)
Contrapositive:
~B-->~A
True, if the original assertion is---if fire always implies smoke, then 'no smoke' implies 'no fire'...and so the existence of 'no smoke' and 'flame' with a correctly used propane torch means that the original assertion is not true for all definitions of fire.
