2. Logical Operators:
• In logic, a logical operators (also called a logical connectives) is a symbol or
word used to connect two or more sentences in a grammatically valid way.
Types of logical Operators:
• Negation • Conjunctions • Disjunctions • Conditional • Bi-conditional;
3. Negation:
• Changing a statement so that it has the opposite meaning and truth
values • Also known as “Not” • The symbol for negation is ‘~’
Example:
P: There is snow on the ground ~P: There is not snow on the ground
Conjunctions:
• A proposition that presents two or more alternative terms, with the
assertion that both are true. • Also known as And. • symbol that we use is
‘^’ (Looks like an A without the middle line – ).
Example:
– P: I found $5
– Q: I crashed my car into a telephone pole
– P^Q: I found $5 AND I crashed my car into a telephone pole.
4. . Disjunctions:
• A proposition that presents two or more alternative terms, with the
assertion that at least one is true. • Also known as “Or” • symbol that we
use is ‘V’
• Example:
– P: The number 3 is odd
– Q: 57 is a prime number
– PVQ: The number 3 is odd OR 57 is a prime number.
Conditionals:
• An conditional is only false when the first statement is true and the
second one is false, otherwise it is true. • Also known as an “If-Then”
Statement • An Conditional for statements P and Q is denoted P=> Q • An
Conditional is read either “If P, then Q” or “P implies Q”
• Example: If you brush every day, you probably won’t get cavities or
5. Bi-conditional:
• Bi-conditionals are true when both statements have the exact same truth
value. • Also known as “ If and only If ” • An Biconditional for statement
P and Q is denoted by P<=> Q • An Bi-conditional is read “P if and only
if Q”
• Example: The candidate becomes president if and only if he wins the
election
