Conditionalstatements andmaterialimplicationPresented by: Majid khanRoll no : 13BBA morning
Conditional statementwhen two statements are combined byplacing the word “if” before the firststatement and “then” before the secondstatement is called conditional statement eg. If Mr. A work hard then he will pass.
Conditional statement We use the arrow → or horseshoe to represent the “if-then” phrase Also called a hypothetical statement
Components of conditionalstatementThere are two components of conditionalstatemento The component statement that follows the “if” is called the antecedento The component statement that follows the “then” is called the consequento If (antecedent), then (consequent)
Conditional StatementA conditional statement does not assert that the antecedent is necessarily true. It only asserts that if the antecedent is true, then the consequent is true. And a conditional statement does not assert that the consequent is necessarily true. It asserts that the consequent is true only if the antecedent is true.
Material implicationA conditional statement describes arelationship between the antecedent andthe consequent. This relationship is called"material implication"Denoted by: “=>” or
For Example If you study hard, then you will pass. Antecedent Consequent => If p, then q.
Material implicationThen the relationship of material implicationbetween p and q is symbolized as p => q+and is read “p implies q”.
Truth Tablep Q P => qT T TT F FF T TF F T“p => q” is false if antecedent p is trueand consequent q is false; otherwise,true.
Logical Implication The consequent follows logically from its antecedent If all humans are mortal and Socrates is a human, then Socrates is mortal.
Definitional Implication The consequent follows the antecedent by definition If Leslie is a bachelor, then Leslie is unmarried.
Causal Implication Theconnection between antecedent and consequent is discovered empirically If I put X in acid, then X will turn red.
Decisional Implication No logical connection nor one by definition between the consequent and antecedent. This is a decision of the speaker to behave in the specified way under the specified circumstances. Is we lose the game, then I’ll eat my hat.