GNED 1101 Chapter Notes - Chapter 1.3: Truth Table

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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 Stateet “I visited Lodo ad 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
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
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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.

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