Consider the propositions p and q. These two propositions can be framed in a compound proposition in two ways having different meanings. The two ways of forming the compound proposition is conjunction and disjunction. Negation is another way by which we invert a proposition.
p: the book is red.
q: the book is fat.
- Disjunction
The disjuction of two propositions p and q is the compound statement p or q, denoted by p ∨ q.
p∨q is the proposition "The book is red or the book is fat."
Truth table for disjunction
- Conjunction
The conjuction of two propositions p and q is the compound statement p and q, denoted by p ∧ q.
p∧q is the proposition "The book is red and the book is fat."
Truth table for conjunction
- Negation
The negation of p is (not p), denoted by ∼p.
∼p means "The book is not red"
Truth table for negation