The phrase "a core of truth" is correct and usable in written English.
It can be used when discussing the fundamental or essential truth within a statement, idea, or belief.
Example: "While the theory has its flaws, there is a core of truth that cannot be ignored."
Alternatives: "an essential truth" or "a fundamental truth".
"No matter how he stuffs his readers with verbiage, it never amounts to a core of truth," he said.
The stories of Taliban cruelty were so many that one felt there was a core of truth in them.
Ironically, one of the many excuses he gave for his election retreat he wants more time to set out his "vision" for Britain has a core of truth.
Mr. Ross's version of "I Can Dream, Can't I?" finds a core of truth in a ballad that nobody else has uncovered.
What do you mean when you say that the early biblical stories do contain a "core of truth?" In the stories of the rise of Israel, there are a lot of stories that have the ring of truth about them, especially in the Book of Judges, which tells of a long, drawn-out struggle with the Canaanites.
A day after Wheeler's statement, he offered his own weak clarification, saying that the show's assertions had been "overstated," but insisting that they contained a core of truth.
The alienated, possessionless freedom of Reacher has a core of emotional truth.
But like most clichés, it survives because there is a core of absolute truth to it that refuses to be dismissed.
That is to say, this gifted pop-jazz theater singer, who appeared on Broadway in "The Life" and off-Broadway as Dinah Washington in "Dinah Was" finds a core of human truth in whatever she sings.
Abandoning Britten and Graham's carefully cultivated style, Mr. Morris is looking for a fresh core of truth in a work that can sometimes seem a labyrinth of stilted artifice.
The myth has staying power because there is a tiny core of truth within it.
