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Democratic U.S. presidential candidates Senator Bernie Sanders and former Secretary of State Hillary Clinton wave as they arrive before of the start of the PBS NewsHour Democratic presidential candidates debate in Milwaukee, Feb. 11, 2016. REUTERS/Jim Young

Former Secretary of State Hillary Clinton and Vermont Sen. Bernie Sanders participated in a highly contentious Democratic presidential debate televised on PBS Thursday night in Milwaukee, with each battling over the issues seemingly quite evenly. They sparred over topics that ranged from race relations to campaign finance to women's rights to senior citizens to foreign relations. Each candidate pointed to their record to back up their series of claims, with both making solid points that stuck to their respective campaigns' core issues. But each seemed to be vying for what would amount to President Barack Obama's third term.

Clinton seemed to maintain a sense of calm and competence while working to emphasize that she and Sanders have similar goals but pointing out that the Vermont senator is not realistic about how to get there. Sanders, in turn, routinely stuck to his campaign's main point of emphasis that economic inequality and big banks were responsible for many of the problems the country has been facing.

One of those problems, he said, was race relations, a topic brought up by PBS moderators Gwen Ifill and Judy Woodruff. Both agreed that much improvement in that arena was sorely needed, but Sanders called it an economic issue. Clinton pointed to "systemic racism" as a primary cause.

“We are seeing the dark side of the remaining systemic racism that we have to root out in our society,” Clinton said. “I think President Obama has set a great example … We have to build on an honest conversation about where we go next.”

On social media, Twitter found that the candidates registered an equal amount of attention in the cyber conversation, at 50 percent each. Their closing statements got a good deal of attention on Twitter, as well.

It wasn't so even when it came to Facebook, though. Sanders was the overwhelming victor, registering 64 percent of volume of conversation at the start to Clinton's 36 percent. Sanders maintained that momentum at the finish, though the margin narrowed, with 57 percent for the Vermont senator and 43 percent for the former secretary of state.

The top social moment during Thursday night's debate, according to Facebook, was when Sanders reminded Clinton of the 2008 election in his closing statement: "One of us ran against Barack Obama; I was not that candidate."

On campaign contributions, Clinton was adamant in defending herself and Obama. "[President Obama] was the recipient of the largest number of donations ever. When it mattered, he stood up and took on Wall Street," she said. "He pushed through and he passed the Dodd-Frank regulation, the toughest regulations since the 1930s. So let’s not imply here that either president Obama or myself would not take on any vested interest… to stand up to do what's best for the American people!"

Foreign relations was also at the forefront of the second half of the debate, and Clinton took the opportunity to specifically call out Republican presidential candidate Donald Trump and his anti-immigrant rhetoric that she says has been "stirring up the demagoguery against American Muslims.”

Clinton also said Obama's choice to select her as his first secretary of state showed the trust he had in her experience, but Sanders fired back that judgment is just as important as experience, citing her senate vote to authorize use of military force in Iraq. "I do not believe a vote in 2002 is a plan to defeat ISIS in 2016. It's very important we focus on the threats we face today," she said. "We need to understand that American Muslims are on the front line of our defense. They are more likely to know what’s happening in their families and their communities, and they need to feel not just invited but welcomed within the American society."

On health care, especially for seniors, Clinton claimed she created the first incarnation of Obamacare, which she called "Hillarycare."

They also argued over the legacy of former Secretary of State Henry Kissinger, whom Sanders had nothing nice to say about while Clinton defended him.

When Clinton said she was ready to assume the presidency, and how that would be a historic moment similar to Obama becoming the nation's first African-American president, Sanders fired back that he too thought his own election would be historic, a statement that was greeted by a rousing ovation from the crowd. "You're not in the White House yet, Hillary," Sanders said matter of factly.

For garnering support from the female voting populace, Clinton appeared ready to pounce. "I have spent my entire adult life working toward making sure that women are empowered to make their own choices, even if that choice is not to vote for me." When she was asked about her seeming lack of appeal among women, she seemed a bit contrite. “Even if that choice is not to vote for me, I believe that it’s most important that we unleash the full potential of women and girls in our society.”

Thursday was the first time Sanders and Clinton met on the debate stage since the Vermont senator finished well ahead of the former secretary of state on the New Hampshire primary, which took place Tuesday night. The two have since been battling it out and vying for the support of one coveted voting demographic in particular: the black vote.

Sanders met with civil rights icon Rev. Al Sharpton the morning after his New Hampshire victory in Harlem at the famous Sylvia's soul food restaurant. While the breakfast didn't result in an official endorsement -- Sharpton said he would decide soon which candidate to support -- the message was clear: Sanders was going hard to secure support from African-American voters. He has already sewn up endorsements from other high profile African-American figures, including activist Cornel West and former NAACP president Ben Jealous.

Clinton, in turn, received the support of the Congressional Black Caucus PAC -- which is different from but related to the actual Congressional Black Caucus itself -- hours before the two Democrats were set to engage in their war of words in Milwaukee, Wisconsin.

One high-profile member of the Congressional Black Caucus spoke out Thursday about his decided support for Clinton by disparaging Sanders' purported participation in the 1960s civil rights movement.

"I never saw him. I never met him," said Lewis, who is himself a civil rights icon in his own right. "I was chair of the Student Nonviolent Coordinating Committee for three years, from 1963 to 1966. I was involved with the sit-ins, the Freedom Rides, the March on Washington, the march from Selma to Montgomery and directed to voter education project for six years. But I met Hillary Clinton. I met President Clinton."