Most of the answers are wrong. Fermat's Little Theorem: If p is prime and a is not divisible by p, then p | a^(p-1) - 1. Which statement is equivalent to Fermat's Little Theorem with all of the quantifiers written more explicitly? A. For all p in N and for all a in N, if p is prime and a is not divisible by p, then there exists m in N such that pm = a^(p-1) - 1. B. There exists p in N such that for all a in N, if p is prime and a is not divisible by p, then there exists m in N such that pm = a^(p-1) - 1. C. For all p in N, there exists a in N such that if p is prime and a is not divisible by p, then there exists m in N such that pm = a^(p-1) - 1. D. For all p in N, there exists a in N such that if p is prime and a is not divisible by p, then for all m in N, we have pm = a^(p-1) - 1. Each of the following statements is true. They follow from Fermat's Little Theorem by some applications of Universal Generalization, Universal Instantiation, Existential Generalization, or Existential Instantiation. For each statement, say which inference rule was used to derive it from a previous statement. Some options can be used more than once. 3 is prime. For all a in N such that a is not a multiple of 3, we have 3 | a^2 - 1. If p is prime and 14 is not divisible by p, then p | 14^(p-1) - 1. There exists a prime p such that for all a in N such that a is not a multiple of p, we have p | a^2 - 1. 14 is not divisible by 3. So, 3 | 14^2 - 1. Let m be a number such that 3m = 14^2 - 1. Fermat's Little Theorem: If p is prime and a is not divisible by p, then p | a^(p-1) - 1. Which statement is equivalent to Fermat's Little Theorem with all of the quantifiers written more explicitly? A. For all p in N and for all a in N, if p is prime and a is not divisible by p, then there exists m in N such that pm = a^(p-1) - 1. B. There exists p in N such that for all a in N, if p is prime and a is not divisible by p, then there exists m in N such that pm = a^(p-1) - 1. C. For all p in N there exists a in N such that if p is prime and a is not divisible by p, then there exists m in N such that pm = a^(p-1) - 1. D. For all p in N there exists a in N such that if p is prime and a is not divisible by p, then for all m in N, we have pm = a^(p-1) - 1. Each of the following statements is true. They follow from Fermat's Little Theorem by some applications of Universal Generalization, Universal Instantiation, Existential Generalization, or Existential Instantiation. For each statement, say which inference rule was used to derive it from a previous statement. Some options can be used more than once. 3 is prime. For all a in N such that a is not a multiple of 3, we have 3 | a^2 - 1. (Universal Generalization) There exists a prime p such that for all a in N such that a is not a multiple of p, we have p | a^2 - 1. (Universal Instantiation) 14 is not divisible by 3. So, 3 | 14^2 - 1. (Existential Generalization) Let m be a number such that 3m = 14^2 - 1. (Existential Instantiation)
