Conditional Statement
Transcript: Conditional Statement Converse, Inverse, Contrapositive by: Hannah Micah Pacheco Match Me! Let us play a game called “Match Me”. You have to match the pictures that I will show you from column A to column B. Column B Column A MATCH ME MATCHING STATEMENTS MATCHING STATEMENTS answers If you are late to school, the teacher will be angry If I got lost, I would look at a map. If you had told me, I would have known. If we had studied more, we would have gotten better grades. If I had a million dollars, I would buy a house If you need me, call my cell phone. If I hadn’t done the homework, I would have lower grades. If my head hurts, then I will take a pill. If it rains, then the ground is wet. Now read the last statement. If it rains, then the ground is wet. Three other statements may be formed from this statement. These are: If the ground is wet, then it rained. If the ground is not wet, then it did not rain. If it does not rain, then the ground is not wet. Which of the four statements are always true? ANALYSIS The four statements given above are called conditional statements or “if-then” statements which is formed by joining the p and q using the words if and then. The “if” part is called the hypothesis (p). It tells us what is given or what is assumed. The “then” part is called the conclusion (q). It tells us what to follow from the assumptions. Statement: It rains the ground is wet. Hypothesis (p): It rains Conclusion(q): The ground is wet If we apply the “if-then” statement, it will become: Conditional Statement: If it rains, then the ground is wet. CONDITIONAL STATEMENTS CONDITIONAL STATEMENT Every conditional statement has three (3) related statements and these are converse, inverse, and contrapositive of the conditional. CONVERSE The CONVERSE of a conditional statement is formed by interchanging the hypothesis and the conclusion. For instance, the converse of p → q is q → p (if q, then p). It may be also true or false. If it rains, then the ground is wet. p q If the ground is wet, then it rained. q p In this case, the conditional is TRUE, but the converse is FALSE. INVERSE The INVERSE of a conditional statement is formed by NEGATING BOTH the hypothesis and conclusion. For instance, the inverse of p → q is ~p → ~q (if not p, then not q). If it rains, then the ground is wet. p q If it does not rain, then the ground is not wet. ~p ~q Is the statement TRUE or FALSE? CONTRAPOSITIVE The CONTRAPOSITIVE of a conditional statement is formed by interchanging the hypothesis and conclusion and NEGATING BOTH. For instance, the contrapositive of p → q is ~q → ~p (if not q, then not p). If it rains, then the ground is wet. p q If the ground is not wet, then it did not rain. ~q ~p Is the statement TRUE or FALSE? Another example Statement: I studied the lesson, I will pass the exam. Hypothesis (p): I studied the lesson Conclusion(q): I will pass the exam. What is the conditional statement using this p and q? If I studied the lesson, then I will pass the exam. p q Is the statement TRUE or FALSE? CONVERSE Statement: I studied the lesson, I will pass the exam. Hypothesis (p): I studied the lesson Conclusion (q): I will pass the exam. Conditional Statement: If I studied the lesson, then I will pass the exam. What is the CONVERSE of this statement? Is the statement TRUE or FALSE? If I passed the exam, then I studied the lesson. q p INVERSE Statement: I studied the lesson, I will pass the exam. Hypothesis (p): I studied the lesson Conclusion (q): I will pass the exam. Conditional Statement: If I studied the lesson, then I will pass the exam. What is the INVERSE of this statement? If I did not study the lesson, then I will not pass the exam. ~p ~q Is the statement TRUE or FALSE? CONTRAPOSITIVE Statement: I studied the lesson, I will pass the exam. Hypothesis (p): I studied the lesson Conclusion (q): I will pass the exam. Conditional Statement: If I studied the lesson, then I will pass the exam. What is the CONTRAPOSITIVE of this statement? If I will not pass the exam, then I did not studied the lesson. ~q ~p Is the statement TRUE or FALSE? Another example Conditional Statement (if p, then q): If a polygon is a square, then it is also a quadrilateral. (True) Converse (if q, then p) If a polygon is a quadrilateral, then it is also a square. (False) Inverse (if not p, then not q): If a polygon is not a square, then it is also not a quadrilateral. (False) Contrapositive (if not q, then not p) If a polygon is not a quadrilateral, then it is also not a square. (True) Is the statement TRUE or FALSE? Another Statement: A guitar player is a musician. Conditional Statement (if p, then q): If you are a guitar player, then you are a musician. (True) Converse (if q, then p) If you are a musician, then you are a guitar player. (False) Inverse (if not p, then not q): If you are not a guitar player, then you are not a musician. (False) Contrapositive (if not q, then not p) If you are not a musician, then you are not a guitar player.” (True) Is the
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