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Jesus Christ is at the core of Mormon faith, an LDS apostle said emphatically on Sunday, and one clear piece of evidence is the Utah-based faith's formal name — The Church of Jesus Christ of Latter-day Saints.

"This is the name by which the Lord will call us at the last day," M. Russell Ballard told more than 20,000 Mormons gathered in the giant Conference Center and millions more watching via satellite and on the Internet. "It is the name by which [Jesus Christ's] church will be distinguished from all others."

In an address during the morning session on the second day of the faith's 181st Semiannual General Conference, Ballard also condemned the use of the term Mormon to describe former members of the church or those who practice polygamy, which the LDS Church abandoned more than 100 years ago.

It leads to confusion, he said.

"Let me state clearly that no polygamist group, including those calling themselves Fundamentalist Mormons or other derivatives of our name," Ballard said, "have any affiliation whatsoever with The Church of Jesus Christ of Latter-day Saints."

Other speakers Sunday discussed the need to be witnesses of Jesus Christ even in adverse situations, the importance of the faith's unique scripture, The Book of Mormon and the balm of Christ's atoning sacrifice for human suffering.

Robert D. Hales, of the Quorum of the Twelve Apostles, who spoke in the morning from his seat and with an oxygen tube, addressed the problem of pain.

"Why is it that the Son of God and his holy prophets and all the faithful saints have trials and tribulations, even when they are trying to do Heavenly Father's will?" he asked. "Why is it so hard, especially for them?"

Learning to cope with adversity brings growth and spiritual strength, said Hales, who didn't return for the afternoon session. "He knows your sacrifices and your sorrows. He hears your prayers. His peace and rest will be yours as you continue to wait upon Him in faith."

Quentin L. Cook, another apostle, also took up the issue of human tragedies.

He described opposite experiences with the ill-fated Titanic: a set of Mormon missionaries scheduled to be on the boat who instead left a day later, and a Provo nurse midwife returning home who went down with the ship.

"Righteousness, prayer and faithfulness will not always result in happy endings in mortality," Cook said in the afternoon. "Adverse results in this mortal life are not evidence of lack of faith or of an imperfection in our Father in Heaven's overall plan. The refiner's fire is real, and qualities of character and righteousness that are forged in the furnace of affliction perfect and purify us and prepare us to meet God."

The Titanic's terrible loss of life was due, in part, because there were not enough lifeboats, the apostle said. "Regardless of the trials we face in this life, the Savior's atonement provides lifeboats for everyone."

Elaine Dalton, president of the church's Young Women's organization, told fathers how they can raise their daughters to be healthy and well-adjusted in a "toxic world."

"By the way you love her mother," she said, "you will teach your daughter about tenderness, loyalty, respect, compassion and devotion."

Dalton urged Mormon fathers to be present in their daughters' lives, to lay out standards and expectations for the girls' successes, and make clear the importance of an education.

"Help her choose music and media that invite the Spirit," the Young Women's leader said, "and is consistent with her divine identity."

Fathers are, by definition, Dalton said, "the guardians of your homes, your wives and your children."

If a teenage daughter does not come home from a date on time, she said, "go get her."

The daughter may resist and say, " You have ruined her social life," Dalton said, "but she will inwardly know that you love her and that you care enough to be her guardian."

Church President Thomas S. Monson returned Sunday to the theme of Latter-day Saints holding fast to their teachings in the face of the world's evolving morals.

"The laws of God remain constant," the 84-year-old LDS leader said as the morning's concluding speaker. "They are not suggestions. They are every bit as requisite today as they were when God gave them to the children of Israel."

In these commandments, Monson said, "we hear the echo of God's voice, speaking to us, here and now."

Thus, said Monson — considered a "prophet, seer and revelator" by nearly 14 million Mormons worldwide — church members know that "morality is not passe, that our conscience is there to guide us, and that we are responsible for our actions."