In predicate as in propositional logic, we use proofs to establish that a conclusion follows validly from a set of premises, and proof in predicate logic has the same structure: we proceed step by step from the premises, in accordance with equivalence rules and rules of inference, until we reach the conclusion. To work with quantifiers, we're going to need several new rules:

• Equivalence rule

• Universal instantiation

• Existential generalization

• Existential instantiation

• Universal generalization

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Comprehension Questions

1.	Which of the following is the quantifier-negation rule?
	a)	(x) (...x...). Therefore, (...a...)
	b)	~(x) (...x...). Therefore, (x) ~(...x...)
	c)	(...a...). Therefore, (x) (...x...)
	d)	(x) (...x...). Therefore, (...a...)
	e)	(...a...). Therefore, (x) (...x...)
2.	Which of the following is the universal instantiation rule?
	a)	(x) (...x...). Therefore, (...a...)
	b)	~(x) (...x...). Therefore, (x) ~(...x...)
	c)	(...a...). Therefore, (x) (...x...)
	d)	(x) (...x...). Therefore, (...a...)
	e)	(...a...). Therefore, (x) (...x...)
3.	Which of the following is the existential generalization rule?
	a)	(x) (...x...). Therefore, (...a...)
	b)	~(x) (...x...). Therefore, (x) ~(...x...)
	c)	(...a...). Therefore, (x) (...x...)
	d)	(x) (...x...). Therefore, (...a...)
	e)	(...a...). Therefore, (x) (...x...)
4.	Which of the following is the existential instantiation rule?
	a)	(x) (...x...). Therefore, (...a...)
	b)	~(x) (...x...). Therefore, (x) ~(...x...)
	c)	(...a...). Therefore, (x) (...x...)
	d)	(x) (...x...). Therefore, (...a...)
	e)	(...a...). Therefore, (x) (...x...)
5.	Which of the following is the universal generalization rule?
	a)	(x) (...x...). Therefore, (...a...)
	b)	~(x) (...x...). Therefore, (x) ~(...x...)
	c)	(...a...). Therefore, (x) (...x...)
	d)	(x) (...x...). Therefore, (...a...)
	e)	(...a...). Therefore, (x) (...x...)

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