Conditional statement and material implication
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Conditional statements relate two statements where the second statement is contingent on the first being true. They are represented by "if-then" phrases or a conditional arrow. The statement before the "if" is called the antecedent, and the statement after the "then" is called the consequent. Material implication describes the relationship between the antecedent and consequent, where a conditional statement is only false if the antecedent is true and consequent is false. There are different types of implications including logical, definitional, causal, and decisional.
Conditional statement and material implication
- 2. Conditional statements and material implication Presented by: Majid khan Roll no : 13 BBA morning
- 3. Conditional statement when two statements are combined by placing the word “if” before the first statement and “then” before the second statement is called conditional statement eg. If Mr. A work hard then he will pass.
- 4. Conditional statement We use the arrow → or horseshoe to represent the “if-then” phrase Also called a hypothetical statement
- 5. Components of conditional statement There are two components of conditional statement o The component statement that follows the “if” is called the antecedent o The component statement that follows the “then” is called the consequent o If (antecedent), then (consequent)
- 6. Conditional Statement A 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.
- 8. Material implication A conditional statement describes a relationship between the antecedent and the consequent. This relationship is called "material implication" Denoted by: “=>” or
- 9. For Example If you study hard, then you will pass. Antecedent Consequent => If p, then q.
- 10. Material implication Then the relationship of material implication between p and q is symbolized as p => q+ and is read “p implies q”.
- 11. Truth Table p Q P => q T T T T F F F T T F F T “p => q” is false if antecedent p is true and consequent q is false; otherwise, true.
- 12. Logical Implication The consequent follows logically from its antecedent If all humans are mortal and Socrates is a human, then Socrates is mortal.
- 13. Definitional Implication The consequent follows the antecedent by definition If Leslie is a bachelor, then Leslie is unmarried.
- 14. Causal Implication Theconnection between antecedent and consequent is discovered empirically If I put X in acid, then X will turn red.
- 15. 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.
- 16. Thank you