1. CSE 2353 – September 4th 2002
Logic

2. Review Propositions Operators Truth Tables Precedence Conditionals
Implication
Others
Truth Tables
Precedence
Conditionals
Contrapositive, Inverse, Converse
Tautologies and Contradictions

3. Operations And (conjunction) ^ Or (inclusive disjunction) v
Xor (exclusive disjunction) v
Not (negation) ~ 
If … then (implication)  
Iff (biconditional) 
Nand |
Nor 
Construct sentences with words

4. Implication If p then q (otherwise q or ~q) Telecomm Example:
“e” = equipped; “s” = in service; “d” = diags
If s then e
If d then e
If s then d

5. Implication Consistency Check() If (s and e) or ~s then
If (d and e) or ~d then
If (s and d) or ~s then
Return success
Return failure

6. Implication Consistency check() Simpler code; multiple return points
If (s and ~e) then return fail
If (d and ~e) then return fail
If (s and ~d) then return fail
Return success
Simpler code; multiple return points

7. Implication Consistency check() Simpler code; no branches; one return.
Val = true;
Val &= (~s or e);
Val &= (~d or e);
Val &= (~s or d);
Return Val;
Simpler code; no branches; one return.

8. Implication Simplest code. Or
Return (~s or e) and (~d or e) and (~s or d); Or
Return ( ~s or d) and (~d or e);

9. Duality Swap t,f Swap ^,v Example (p ^ q) v ~p Dual (p v q) ^ ~p
If expressions are equivalent, so are duals

10. Arguments
If you insulted Bob then I’ll never speak to you again. You insulted Bob so I’ll never speak to you again.
Premise
Conclusion

11. Arguments
If you are a mathematician then you are clever. You are clever and rich. Therefore If you are rich then you are a mathematician.
Premise
Conclustion

12. Laws Idempotent Commutative Associative Absorption Distributive
Involution
De Morgan’s
Complement

13. Laws Example
Prove that (~p ^ q) v ~(p v q)  ~p.

14. Predicates Universal Quantifier  All rats are grey R(x): x is a rat.
G(x): x is grey
(x)[R(x) G(x)]

15. Predicates Existential Quantifier  Some rats are grey
R(x): x is a rat.
G(x): x is grey
(x) [R(x) ^ G(x)]

16. Examples
Some children didn’t apologize

17. Examples
All students who did their homework passed the final exam.

18. Examples
Some body set off the fire alarm and everybody left the building.

19. 2 Place Predicates P(x,y) x + y = 7 (x)(y) [ P(x,y) ] is true
(y) (x) [ P(x,y) ] is not true

20. Negation, Specification, and Generalization
~(x)[F(x)] =
~(x)[G(x)] =