Scrabble Dictionary

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Yes, consent is playable

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Found in the following dictionaries

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SOWPODS (Collins Scrabble Words)
OTCWL2014 (NASPA Word List 2014)
TWL06 (NASPA List 2006)

"Consent" Definition

noun

Acceptance or approval of what is planned or done by another; acquiescence. See Synonyms at permission.
Agreement as to opinion or a course of action: She was chosen by common consent to speak for the group.
Compliance in or approval of what is done or proposed by another .
Agreement as to action or opinion.
Voluntary agreement by a people to organize a civil society and give authority to the government.

verb-intransitive

Archaic To be of the same mind or opinion.
To give assent, as to the proposal of another; agree. See Synonyms at assent.

verb

To give assent or approval .
To be in concord in opinion or sentiment.