∀xP(x)___________∴P(c)
The first part of the expression, ∀xP(x), is a universal quantification in predicate logic
The first part of the expression, ∀xP(x), is a universal quantification in predicate logic. It means that “for all x, P(x) is true.” This statement asserts that the predicate P is true for every possible value of x in its domain.
The second part of the expression, ∴P(c), represents a logical conclusion based on the previous statement. The symbol ∴ means “therefore,” indicating that we can infer the truth of P(c) based on the universal statement ∀xP(x).
To put it into words, if we know that P is true for every value of x, it follows that P is also true for a specific value c. The inference is made because c is considered within the same domain as x, and since P holds true for all values of x, it must also be true for c.
In simpler terms, if a statement is true for every possible value, it must also be true for a specific value.
More Answers:
The Universal Quantifier Principle and Implication | If P(c) holds true for any value of c, then ∀xP(x)Logical Implication | If There Exists an Element x such that P(x) is True, Then P(c) is True for Some Element c
Understanding Conditional Statements and Proving the Negation | qp → q and Contradiction