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SUMTER, S.C. – Hillary Clinton and Bernie Sanders are seeking to appeal to their core constituencies — she to women and he to young people — as they seek votes from African-Americans in South Carolina.

The divide was on vivid display Monday afternoon at the Mount Zion Missionary Baptist Church here, as five mothers in the Black Lives Matter movement spoke powerfully about their support for Mrs. Clinton – including one who had some words for her granddaughter, who is backing Mr. Sanders.

Gwen Carr, whose son Eric Garner was killed when a New York City police officer put him in a chokehold in 2014, described her son’s death during a Clinton campaign event here and praised Mrs. Clinton for devoting time listening to her and promising to overhaul the criminal justice system.

Referring to police officers and her son, Ms. Carr said, “They would have never done that to him, if he was a white Eric Garner in the suburbs.”

“This racial profiling, it has to stop. We all have to be treated like human beings,” Ms. Carr said to an audience of about 25 people, mostly older African-American women. “We know that all lives matter, but we have to make them understand that our life is just as important as anyone else’s life. Hillary Clinton understands this.”

Ms. Carr’s granddaughter, Erica Garner, who is Eric Garner’s oldest child, campaigned for Mr. Sanders in South Carolina last week and introduced him at a rally at the University of South Carolina. Ms. Garner also made an endorsement video that included footage of her father’s death on a Staten Island sidewalk. Parts of that video are used in a Sanders campaign commercial running in South Carolina, in which Ms. Garner hails Mr. Sanders as “a protester” and says he is “not scared to go up against the criminal justice system.”

Ms. Carr, asked about her granddaughter’s position, smiled warmly and said she hoped young people wouldn’t become caught up in the Sanders movement without looking closely at both candidates.

“You know how young people are,” Ms. Carr said. “Sometimes they get fed something and they believe it. The only thing I can say is, do your research. Do your research and then make your decision. Don’t make your decision because your friend and peers are doing this. Look at Bernie and what Bernie has done. Look at Hillary’s track record and see how it weighs out.”

Mrs. Clinton was not at the event; she was off the campaign trail attending fund-raisers on Monday. But Ms. Carr and the other women, including the mothers of Trayvon Martin and Sandra Bland, are speaking at events for Mrs. Clinton around the state on Monday and Tuesday.

Mrs. Clinton and her husband, former President Bill Clinton, are popular with many African-Americans, who are expected to make up about half of the Democratic primary electorate here on Saturday. But Mr. Sanders proved far more popular with college students and voters in their 20s in Nevada, New Hampshire, and Iowa, the first three states that have voted in the Democratic nomination fight. Many of those young Sanders supporters have been white. The South Carolina primary will be the first significant test of Mr. Sanders’s support among young African-American voters.