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The sentence "mutual understanding between" is correct and can be used in written English.
It is used to refer to the general understanding that two people or groups have of each other. For example, "It is important to have a mutual understanding between spouses for a healthy marriage."
Exact(59)
They found a mutual understanding between themselves and married.
We need to work together to foster dialogue and mutual understanding between communities".
This leads, in his view, to resentment, which undermines the possibility of mutual understanding between groups.
Kim said he hoped sports exchange would promote "mutual understanding between the people of the two countries", KCNA said.
He called the concert "an important occasion to open a chapter of mutual understanding between the two countries".
"The K.G.B. were Slavs, yet they were also European, and there was a mutual understanding between us and them.
A Beijing Olympics would "boost exchanges and mutual understanding between the Chinese and other civilisations of the world," Xi said.
The festival brought musicians, dancers, artists and artisans from India to various venues in the UK, developing a new mutual understanding between the two countries.
But he conceded that a lack of mutual understanding between the sectors – especially between GPs and social care – was a barrier to joining up care.
A Trump presidency surely means the end of any collaboration or mutual understanding between the White House and Black Lives Matter activists and reformers.
His hope that a mutual understanding between Protestants and Roman Catholics would bring about an undivided church has inspired modern ecclesiastics.
More suggestions(17)
mutual respect between
mutual harmony between
mutual comprehension between
mutual knowledge between
mutual intelligibility between
mutual appreciation between
international understanding between
mutual partnership between
mutual sympathy between
mutual agreements between
shared understanding between
mutual estrangement between
mutual mistrust between
mutual confidence between
mutual distrust between
mutual society between
mutual one between
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com