If and then statements

If and then statements-grade 8 mathematics

1. If-then Statements

2. Conditional Statement A logical type of statement that has two parts: a hypothesis and a conclusion. Conditional can be written in IF-THEN form. A conditional statement is a compound statement of the form “If p then q“ where p and q are statements.

3. The first statement, p, is called the hypothesis and usually begins with if, while the second statement, q, which usually begins with then is called the conclusion. If HYPOTHESIS , then CONCLUSION . If _____________, then ______________. Hypothesis (p) Conclusion (q)

4. Hypothesis- It states the given facts that are assumed to be true. Conclusion- What need to be proven or established. Implication- is a statement formed by hypothesis and conclusion. “If p, then q.” “p q”

5. Let us connect the given input and output using the if-then form. Input: I studied for my math test. Output: I got a good grade. So, using the if- then statement, the input is the hypothesis of the statement and the output is the conclusion of the statement. Answer: If I studied for my math test , then I got a good grade .

6. Let us connect the given input and output using the if-then form. Input: It is raining. Output: We need to use our umbrella. So, using the if- then statement, the input is the hypothesis of the statement and the output is the conclusion of the statement. Answer: If it is raining , then we need to use our umbrella .

7. Example #1 If a number is greater than zero, then the number is positive. Hypothesis: The number is greater than zero. Conclusion: The number is positive.

8. Example #2 If it’s a quadrilateral, then it has four sides. Hypothesis: It’s a quadrilateral. Conclusion: It has four sides.

9. Example #3 If 3(n+1) = 6, then n= 1. Hypothesis: 3(n+1) = 6 Conclusion: n= 1

10. Example #4 Getting enough sleep is good for your health. Hypothesis: Getting enough sleep Conclusion: Good for your health.

11. Example #5 An integer that ends in 1,3,5,7 and 9 is an odd integer. Hypothesis: An integer that ends in 1,3,5,7 and 9 Conclusion: It is an odd integer

12. Example #6 All prime number are numbers with no other factor aside from 1 and itself. Hypothesis: Numbers with no other factor aside from 1 and itself Conclusion: It is a prime number

13. Example #7 You have a fever if your body temperature is above 37.6 ℃ Hypothesis: Your body temperature is above 37.6 ℃ Conclusion: You have a fever.

14. Transforming a Statement into an Equivalent If-then Statement

15. You learned how to identify the hypothesis and conclusion of a given conditional statement. But not all conditional statements are written in if-then form where the hypothesis-conclusion can be easily identified. In some conditional statements, conclusions are written before the hypothesis.

16. Determining the Inverse, Converse and Contrapositive of an If-then Statement

17. Every conditional statement has three (3) related statements and these are converse, inverse and contrapositive conditional.

18. Converse To write the converse of a conditional statement, simply interchange the hypothesis and the conclusion. That is, the then part becomes the if part and the if part becomes the then part.

19. Inverse To write the inverse of a conditional statement, simply negate both the hypothesis and conclusion.

20. Contrapositive To form the contrapositive of a conditional statement, first, get its inverse. Then, interchange its hypothesis and conclusion.

21. More Examples

22. Converse

23. Biconditional Statement

24. Inverse

25. Contrapositive

26. Exercises

27. Exercises “A guitar is a musician”

28. Logically Equivalent

29. Directions: Determine the following statement if it is converse, inverse or contrapositive of the given conditional (if-then) statement. Conditional statement: If it’s a right angle, then its measure is 90 degrees _________1. If the measure of the angle is 90 degrees, then it is a right angle. _________2. If the measure of the angle is not 90 degrees, then it is not a right angle. _________3. If the angle is not a right angle, then its measure is not 90 degrees

30. Directions: Determine the following statement if it is converse, inverse or contrapositive of the given conditional (if-then) statement. Conditional statement: If you do your homework, then you will pass in Mathematics. _________4. If you do not pass in Mathematics, then you do not do your homework. _________5. If you passed in Mathematics, then you did your homework. _________6. If you do not do your homework, then you will not pass in Mathematics.

31. For items 7-10, refer to the statement below. “If a figure is a square, then it has 4 equal sides.” 7. What is the hypothesis of the statement? A. equal sides B. is a square C. a figure is a square D. it has 4 equal sides

32. For items 7-10, refer to the statement below. “If a figure is a square, then it has 4 equal sides.” 8. If a figure is not square, then it doesn’t have 4 equal sides. A. contrapositive B. converse C. if-then D. inverse

33. For items 7-10, refer to the statement below. “If a figure is a square, then it has 4 equal sides.” 9. If a figure has 4 equal sides, then it is a square. A. conclusion B. contrapositive C. converse D. inverse

34. For items 7-10, refer to the statement below. “If a figure is a square, then it has 4 equal sides.” 10. If a figure doesn’t have 4 equal sides, then it is not a square. A. contrapositive C. hypothesis B. converse D. inverse