COSI 29a Chapter Notes - Chapter 1.3: Existential Quantification, Universal Quantification, Fierce Creatures

• School: Brandeis University
• Department: Computer Science
• Course: COSI 29a
• Professor: Cherniack Mitch

Document Summary

The predicate refers to a property that the subject can have. For example, in > 3 the subject is and the predicate is > 3. The universal quantification means that p() is true for all values of in the domain, aka. Ex: let p() be + 1 > . What is the truth value of the quantification (cid:1842)(cid:4666)), where the. Note that is the universal quantifier, so the quantification (cid:1842)(cid:4666)) means for all (cid:1842)(cid:4666)). Since + 1 > is true for all real numbers , the quantification (cid:1842)(cid:4666)) is true. Since < 2 is not true for the value = 3, < 2 is not true for all real numbers , the quantification (cid:1842)(cid:4666)) is false. The existential quantification means that p() is true if there is an that is true. What is the truth value of the quantification (cid:1842)(cid:4666)(cid:4667), where the domain is. Note that is the existential quantifier, so the quantification (cid:1842)(cid:4666)(cid:4667) means for at least one (cid:1842)(cid:4666)(cid:4667).