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MEMPHIS, Tenn. -- Two candidates vying to become Tennessee's next governor faced off at the University of Memphis Tuesday evening in the first of three scheduled debates.

Republican businessman and political newcomer Bill Lee and the Democrat Karl Dean, the former mayor of Nashville, both took time during the debate to pay tribue to slain Memphis business leader Phil Trenary.

But the candidates couldn't find common ground on how prevent the types of violent crimes that claimed his life. Dean took aim at guns, proposing a ban on gun ownership for people with mental illness or criminal histories, including domestic violence.

"That’s not taking guns away from people. That’s merely keeping guns out of the hands of people who are dangerous and that’s common sense," he said.

But Lee said Dean's proposal would infringe on a fundamental American right and sidesteps the underlying problem.

"We need to not approach that. we need to approach the person with domestic violence and addressing that rather than taking away their guns," Lee told WREG following the debate.

The candidates put further distance between each other on the issue of Medicaid.

Dean wants to expand the state's system, but Lee argues the system is too broken to be expanded.

"Expanding a broken, flawed system by taking federal money and moving something down the road that is fundamentally flawed, I believe, is a mistake for Tennessee," Lee said.

On education, there was some agreement between the candidates. Both were critical of the state's TN Ready testing system.

But Dean differed from Lee with his opposition to government vouchers for private schools.

"I think vouchers actually take money out of the public school system, move it into a private system and there’s no guarantee on the quality of those schools," Dean said.

The next debate takes place next week in East Tennessee.