Category: Proposition and Logic

5 Posts

Basic Counting Principles
Sum Rule Principle Suppose that an event E can occur in m ways and a second event F can occur in n ways and suppose both events cannot occur simultaneously. Then E or F can occur in m+n ways. Example - If 5 male professors and 8 female professors teach…
Logical Equivalent
Two logical statements p and q are said to be logical equivalents. It is denoted by p≡q when if p⇔q is a tautology. Note: Do not write p = q; instead write p ≡ q. Note: It doesn't mean that p and q are equal. Since p and q are different…
Tautologies and Contradiction
Tautologies A proposition p is a tautology when it is true in all situations. P tautology contains only the True in the field of the column of its truth table. Example: (p⟶q) ↔(∼q⟶∼p) is a tautology pqp⟶q~p~q~q⟶~p(p⟶q) ↔(∼q⟶∼p)TTTFFTTTFFFTFTFTTTFTTFFTTTTT So the (p⟶q) ↔(∼q⟶∼p) is containing True in all of its rows.…
Logical Operations
Negation Negation means the opposite of the original statement. If p is the statement, then the negation of p will be denoted by ~p and read as "It is not the case that p". So if p is true then ~p will be false and vice versa. Example - If…
Proposition and Compound Proposition
A proposition or a statement or a logical sentence is a declarative sentence that can be either true or false. Example of Propositions Jawaharlal Nehru was the first prime minister of India. Today is Monday. Example of Non-Propositions What is your name? Please come in. Propositional Variable The lowercase letters…