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 Maths then the students can …
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 statements, they cannot be the …
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 p q p⟶q ~p ~q ~q⟶~p (p⟶q) ↔(∼q⟶∼p) T T T F F T T T F F F …
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 the statement p is “New …
A proposition or a statement or a logical sentence is a declarative sentence that can be either true or false. Example of Propositions Example of Non-Propositions Propositional Variable The lowercase letters starting with P are used to represent the proposition. Example p: Mahatma Gandhi is the father of India. q: 2+2 = 4 Compound Propositions …
