Final answer:
Antonio and Sylvia need to petition for an election with the NLRB. The election will be held as they have the support of at least thirty percent of the workers, which is the minimum requirement under U.S. labor law.
Step-by-step explanation:
When Antonio and Sylvia present union authorization cards with signatures from sixty percent of Piedmont Manufacturing's employees, they are demonstrating significant support for the union amongst the workforce.
According to the federal labor laws in the United States, an employer is not legally mandated to recognize a union based solely on authorization cards. Rather, an official election must be held through the National Labor Relations Board (NLRB) to confirm the desire for union representation.
If Sylvia and Antonio wish to move forward with forming a union after Piedmont Manufacturing's refusal to recognize the union, the correct course of action would involve filing a petition for an election with the NLRB.
If they can demonstrate that at least thirty percent of the workers support the union through signed authorization cards, which they already have with sixty percent, an election will be mandated. Therefore, the correct option in regards to their next step, assuming U.S. labor law applies, is:
C. an election will be held if Sylvia and Antonio can show that at least thirty percent of the workers support a union.