If and 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.
- 18. Transforming a Statement into an Equivalent If- then Statement
- 19. 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.
- 36. Every conditional statement has three (3) related statements and these are converse, inverse and contrapositive conditional.
- 38. 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.
- 39. Inverse To write the inverse of a conditional statement, simply negate both the hypothesis and conclusion.
- 40. Contrapositive To form the contrapositive of a conditional statement, first, get its inverse. Then, interchange its hypothesis and conclusion.
- 43. More Examples
- 44. Converse
- 49. Inverse
- 50. Contrapositive
- 51. Exercises
- 52. Exercises “A guitar is a musician”
- 56. 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
- 57. 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.
- 58. 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
- 59. 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
- 60. 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
- 61. 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