Background: Mumtaz Mahal (Urdu: mumtz mHal ), ([mum'ta:z me'hel]; meaning "the Exalted One of the palace"; Arjumand Banu; 27 April 1593 - 17 June 1631) was Empress consort of the Mughal Empire from 19 January 1628 to 17 June 1631 as the chief consort of the Mughal emperor Shah Jahan. The UNESCO World Heritage Site Taj Mahal in Agra, often cited as one of the Wonders of the World, was commissioned to act as her final resting place. Mumtaz Mahal was born Arjumand Banu Begum in Agra to a family of Persian nobility.
Context: Mumtaz Mahal was betrothed to Shah Jahan around 30 January 1607, when she was 14 years old at the time and he was 15. They were, however, married five years after the year of their betrothal on 30 April 1612 in Agra. The marriage was a love-match. After their wedding celebrations, Shah Jahan, "finding her in appearance and character elect among all the women of the time", gave her the title "Mumtaz Mahal" Begum ("the Exalted One of the Palace"). During the intervening years between their betrothal and marriage, Shah Jahan had gotten married to his first wife, Princess Kandahari Begum in 1609 and in 1617, after marrying Mumtaz, took a third wife, Izz-un-Nissa Begum (titled Akbarabadi Mahal), the daughter of a prominent Mughal courtier. According to the official court historians, both the marriages were political alliances.  By all accounts, Shah Jahan was so taken with Mumtaz that he showed little interest in exercising his polygamous rights with his two other wives, other than dutifully siring a child with each. According to the official court chronicler, Motamid Khan, as recorded in his Iqbal Namah-e-Jahangiri, the relationship with his other wives "had nothing more than the status of marriage. The intimacy, deep affection, attention and favour which Shah Jahan had for Mumtaz exceeded what he felt for his other wives." Likewise, Shah Jahan's historian Inayat Khan commented that 'his whole delight was centered on this illustrious lady [Mumtaz], to such an extent that he did not feel towards the others [i.e. his other wives] one-thousandth part of the affection that he did for her.'  Mumtaz had a loving marriage with Shah Jahan. Even during her lifetime, poets would extol her beauty, grace, and compassion. Despite her frequent pregnancies, Mumtaz travelled with Shah Jahan's entourage throughout his earlier military campaigns and the subsequent rebellion against his father. She was his constant companion and trusted confidant, leading court historians to go to unheard lengths to document the intimate and erotic relationship the couple enjoyed. In their nineteen years of marriage, they had fourteen children together (eight sons and six daughters), seven of whom died at birth or at a very young age.
Question: Did they have children?

Answer:
they had fourteen children together (eight sons and six daughters), seven of whom died at birth or at a very young age.