The difference between Mutually and Together
When used as adverbs, mutually means in the same way, each to the other, whereas together means at the same time, in the same place.
Together is also adjective with the meaning: coherent.
check bellow for the other definitions of Mutually and Together
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Mutually as an adverb:
in the same way, each to the other; reciprocally
Examples:
"The contract was mutually binding."
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Mutually as an adverb:
in a shared manner; equally; affecting all parties the same way
Examples:
"The adventure was mutually beneficial."
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Together as an adverb:
At the same time, in the same place; in close association or proximity.
Examples:
"We went to school together."
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Together as an adverb:
Into one place; into a single thing; combined.
Examples:
"He put all the parts together."
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Together as an adverb:
In a relationship or partnership, for example a business relationship or a romantic partnership.
Examples:
"Bob and Andy went into business together.  Jenny and Mark have been together since they went on holiday to Mexico."
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Together as an adverb:
Without intermission or interruption; continuously; uninterruptedly.
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Together as an adjective (colloquial):
Coherent; well organized.
Examples:
"He's really together."