Question

What is the rule of inference used to conclude that ∀xP(x) is true when a particular element c with P(c) is true?

Answer 1

The rule of inference used to conclude that ∀xP(x) is true when a particular element c with P(c) is true is called Universal Instantiation in mathematics.

Step-by-step explanation:

In mathematics, the rule of inference used to conclude that ∀xP(x) is true when a particular element c with P(c) is true is called Universal Instantiation. This rule allows us to infer that the predicate P holds for all elements in a given domain (represented by the universal quantifier ∀x) based on the assertion that it holds for a specific element (represented by the particular element c with P(c)).

To use Universal Instantiation, we follow these steps:

1. Start with the assumption that ∀xP(x) is true.
2. Introduce a particular element c with P(c) as an additional premise.
3. Conclude that P(c) is true for a specific element c using the rule of Universal Instantiation.