Etymology
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Words related to forgive

for- 

prefix usually meaning "away, opposite, completely," from Old English for-, indicating loss or destruction, but in other cases completion, and used as well with intensive or pejorative force, from Proto-Germanic *fur "before, in" (source also of Old Norse for-, Swedish för-, Dutch ver-, Old High German fir-, German ver-); from PIE *pr-, from root *per- (1) "forward," hence "in front of, before, toward, near, against."

In verbs the prefix denotes (a) intensive or completive action or process, or (b) action that miscarries, turns out for the worse, results in failure, or produces adverse or opposite results. In many verbs the prefix exhibits both meanings, and the verbs frequently have secondary and figurative meanings or are synonymous with the simplex. [Middle English Compendium]

Probably originally in Germanic with a sense of "forward, forth," but it spun out complex sense developments in the historical languages. Disused as a word-forming element in Modern English. Ultimately from the same root as fore (adv.). From its use in participles it came to be an intensive prefix of adjectives in Middle English (for example Chaucer's forblak "exceedingly black"), but all these now seem to be obsolete.

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*ghabh- 
also *ghebh-, Proto-Indo-European root meaning "to give or receive." The basic sense of the root probably is "to hold," which can be either in offering or in taking.

It forms all or part of: able; avoirdupois; binnacle; cohabit; cohabitation; debenture; debit; debt; dishabille; due; duty; endeavor; exhibit; exhibition; forgive; gavel; gift; give; habeas corpus; habiliment; habit; habitable; habitant; habitat; habitation; habitual; habituate; habituation; habitude; habitue; inhabit; inhibit; inhibition; malady; prebend; prohibit; prohibition; provender.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit gabhasti- "hand, forearm;" Latin habere "to have, hold, possess," habitus "condition, demeanor, appearance, dress;" Old Irish gaibim "I take, hold, I have," gabal "act of taking;" Lithuanian gabana "armful," gabenti "to remove;" Gothic gabei "riches;" Old English giefan, Old Norse gefa "to give."
pardon (n.)

c. 1300, pardoun, "papal indulgence, forgiveness of sins or wrongdoing," from Old French pardon, from pardoner "to grant; forgive" (11c., Modern French pardonner), "to grant, forgive," and directly from Medieval Latin perdonum, from Vulgar Latin *perdonare "to give wholeheartedly, to remit," from Latin per "through, thoroughly" (from PIE root *per- (1) "forward," hence "through") + donare "give as a gift," from donum "gift," from PIE *donum "gift," from root *do- "to give."

Meaning "a passing over of an offense without punishment" is from c. 1300, also in the strictly ecclesiastical sense; the sense of "pardon for a civil or criminal offense; release from penalty or obligation" is from late 14c., earlier in Anglo-French. Weaker sense of "excuse for a minor fault" is attested from 1540s. To beg (one's) pardon "ask forgiveness" is by 1640s.

Strictly, pardon expresses the act of an official or a superior, remitting all or the remainder of the punishment that belongs to an offense: as, the queen or the governor pardons a convict before the expiration of his sentence. Forgive refers especially to the feelings; it means that one not only resolves to overlook the offense and reestablishes amicable relations with the offender, but gives up all ill feeling against him. [Century Dictionary]
forgiving (adj.)
"inclined to forgive," 1680s, from present participle of forgive. Related: Forgivingness.
forgave 
past tense of forgive (q.v.).
forgivable (adj.)
1540s, from forgive + -able. Related: Forgivably.
forgiveness (n.)
Old English forgiefnes, forgifennys "pardon, forgiveness, indulgence," from past participle of forgifan (see forgive) + -ness. Contracted from *forgiven-ness. Middle English also had forgift (early 14c.).
unforgiven (adj.)
early 15c., from un- (1) "not" + past-participle adjective from forgive (v.). Old English had unforgifen.
unforgiving (adj.)
1713, from un- (1) "not" + present-participle adjective from forgive. Old English had unforgifende.