Logic Statements

Hypothesis and Conclusion

• Hypothesis: The condition of the statement that must be fulfilled for the conclusion to be true.

  • Located in the sentence after "IF."

• Conclusion: The outcome that occurs once the hypothesis is confirmed.

  • Located in the sentence after "THEN."

• Conditional Statements: Consist of a hypothesis and a conclusion.

  • Form: A → B.

Variations of Conditional Statements

1. Converse: B → A

   • Definition: Switching the placement of the hypothesis and conclusion.

   • Example: If B, then A.

2. Contrapositive: -B → -A

   • Definition: Negating both the hypothesis and conclusion.

   • Example: If not B, then not A.

3. Inverse: -A → -B

   • Definition: Negating the hypothesis and conclusion.

   • Example: If not A, then not B.

Conditional Statement Structure

• Form: A → B

• Example: IF you give a mouse a cookie, THEN he’s going to ask for a glass of milk.

• Structure of Conditional Statement:

  • If hypothesis, THEN conclusion.

Converse Statements

• Definition: Switching the hypothesis and conclusion.

• Example: If he asks for a glass of milk, THEN you gave a mouse a cookie.

• Form: B → A.

Inverse Statements

• Definition: Negating both the hypothesis and conclusion.

• Example: If you DON’T give a mouse a cookie, THEN he’s NOT going to ask for a glass of milk.

• Form: -A → -B.

Contrapositive Statements

• Definition: Switching and negating the hypothesis and conclusion.

• Example: If he DOES NOT ask for a glass of milk, THEN you DID NOT give a mouse a cookie.

• Form: -B → -A.