Lesson 2: Logical Connections-Prelim

Logical Connections

In ordinary language connectives are used in combining sentences.

combines proposition
combines the truth value of proposition

Logical connections does two things:

p∧q

Conjunction

pvq

Disjunction

-p

Negation

p→q

Conditional

Antecedent

If p

Consequent

then q

p↔q

Biconditional

Truth Functionality

Rules on how logical connectives combine the truth value of proposition.

p=T when -p=F
p=F when -p=T

In Negation (opposite)

p∧q=T when Both p and q are TRUE.
p∧q=F when At least one of the variable is FALSE.

In Conjunction (and)

pvq=T when At least one is TRUE.
pvq=F when both p and q are FALSE

In Disjunction (or)

p→q=T when both p is FALSE, both p and q are TRUE, and both FALSE
p→q=F when the antecedent (p) is TRUE and the consequent (q) is FALSE.

In Conditional (if, then)

-p→-q

Inverse Statement

q→p

Converse Statement

-q→-p

Contrapositive Statement

p↔q=T when p and q have the SAME TRUTH VALUE.
p↔q=F when p and q have DIFFERENT TRUTH VALUE.

In Biconditional (if and only if)

p⊕q=T when exactly one is TRUE.
p⊕q=F when both are TRUE and both are FALSE.

in Exclusive OR (EXOR)