SKILLS ASSIGNMENT 3: NECESSARY & SUFFICIENT CONDITIONS Due: Friday, 7/8, in class Necessary & Sufficient Conditions A is a sufficient condition for B means that: The occurrence of A is enough to bring about B. Given A, B will occur. If A, then B. Examples: Ann's having a daughter is a sufficient condition for her being a mother. Rain is a sufficient condition for the streets being wet. Being an odd number is a sufficient condition for being a number. A is a necessary condition for B means that: B requires A. A is required for B. In order for B to occur, A must occur. B cannot occur without A. If B, then A. Examples: The presence of oxygen is a necessary condition for there being a fire. Having a ticket is necessary to win the lottery. Being an enclosed figure with four sides equal in length is a necessary condition of being a square. Being less than 100 is a necessary condition of being less than 50. Note: B's being a necessary condition of A is equivalent to A's being a sufficient condition of B (and vice versa). Sometimes, A is both a necessary and sufficient condition for B. A iff B. A if and only if B. A just in case B. Examples: Being the 4th of July is a necessary and sufficient condition of being Independence Day in the US. Being divisible by two is a necessary and sufficient condition of being an even number. There is a supplemental reading on necessary and sufficient conditions posted on Catalyst, if you need additional explanation. Assignment: For each of the following, indicate if the statement is true or false. If false, explain why it's false. Please type out your answers on a separate piece of paper. 1. x's being a square is a sufficient condition for x's being a rectangle. 2. x's being a square is a necessary condition for x's being a rectangle. 3. x's being a rectangle is a sufficient condition for x's being a square. 4. x's being a rectangle is a necessary condition for x's being a square. 5. x's being a mother is a sufficient condition for x's being a female. 6. x's being a mother is a necessary condition for x's being a female. 7. x's being a female is a sufficient condition for x's being a mother. 8. x's being a female is a necessary condition for x's being a mother. 9. x's being greater than 15 is a sufficient condition for x's being less than 20. 10. x's being greater than 15 is a necessary condition for x's being less than 20. 11. x's being less than 20 is a sufficient condition for x's being greater than 15. 12. x's being less than 20 is a necessary condition for x's being greater than 15. 13. x's being less than 12 is a sufficient condition for x's being less than 20. 14. x's being less than 12 is a necessary condition for x's being less than 20. 15. x's being less than 20 is a sufficient condition for x's being less than 12. 16. x's being less than 20 is a necessary condition for x's being less than 12. 17. x's having two arms is a sufficient condition for x's being a human being. 18. x's having two arms is a necessary condition for x's being a human being. 19. x's wanting to do a is a sufficient condition for x's doing a. 20. x's wanting to do a is a necessary condition for x's doing a. 21. x's being an equilateral rectangle is a sufficient condition for x's being a square. 22. x's being an equilateral rectangle is a necessary condition for x's being a square.