1. Mathematics for Computer Science MIT 6.042J/18.062J
Predicates & Proof

2. Propositions with variables
Predicates
Predicates are
Propositions with variables
Example:

3. Predicates
For x = 1 and y = 3, is true
For x = 1 and y = 4, is false
is true

4. Quantifiers
For ALL x
There EXISTS some y

5. Quantifiers
x, y range over Domain of Discourse
True over Domain

6. Quantifiers
True over Domain
False over Domain

7. True over positive real numbers, False over negative real numbers,
Quantifiers
True over positive real numbers,
False over negative real numbers,

8. Validity
True no matter what
predicate Q is,
the Domain is.

9. Problems
Class Problems 1-3