# GNED 1101 Chapter Notes - Chapter 1.3: Truth Table

1.3 Truth Tables

Negation Tables

The negation of a true statement is a false statement and vice versa, this can be expressed in tables

Or

Combining the two tables results in the Truth Table for Negation. It simply expresses the idea that p is the

opposite truth value of p.

P

p

T

F

F

T

Conjunction Tables

The Statement “I visited London and I visited Paris has four possible truth values

o If you visited both cities than both p and q are true. If both p and Q are true , then the conjunction p

q is true

P q

P Q

T T

T

o If you visited London and lied about visiting paris then p is true, and q is false. So p q is false. If P is

true and q is false then the conjunction is false

P Q

P Q

T F

F

o Vice Versa, if London was not visited and Paris was then p is false and q is true. If p is false and q is

true the conjunction p q is false

P Q

P Q

F T

F

o If you visited neither cities and thus both p and q are false, then the statement p q is false

P Q

P Q

F F

F

**** Thus, a conjunction is only true when both simple statements are true. Thus as soon as you find one simple

statement in a conjunction that is false, then the conjunction is false

Statements making up compound statements are called component statements

Disjunction

An or statement is true in every case except when both component statements are false

P Q

P Q

T T

T

T F

T

F T

T

F F

F

P

p

T

F

P

p

F

T

## Document Summary

The negation of a true statement is a false statement and vice versa, this can be expressed in tables. Combining the two tables results in the truth table for negation. It simply expresses the idea that p is the opposite truth value of p. The state(cid:373)e(cid:374)t i visited lo(cid:374)do(cid:374) a(cid:374)d i visited paris has four possible truth values. If you visited both cities than both p and q are true. If both p and q are true , then the conjunction p q is true. If you visited london and lied about visiting paris then p is true, and q is false. If p is true and q is false then the conjunction is false. F: vice versa, if london was not visited and paris was then p is false and q is true. If p is false and q is true the conjunction p q is false.