DO NOW Take a blank notecard from the front bookshelf. Explain why the following statements are false. If you live in California, you live in Watts If.

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Presentation transcript:

DO NOW Take a blank notecard from the front bookshelf. Explain why the following statements are false. If you live in California, you live in Watts If the ground is wet, then it has been raining.

Introduction to Logic Logic and Reasoning

Today’s Objectives Use counterexamples to disprove conditional statements. Explain the relationship between hypothesis and conclusion. Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. Use Problem Solving Skills

Conditional Statement An if-then statement Symbolized by p –> q Which p is a hypothesis and q is a conclusion.

Making a statement conditional. Get rid of the word “all” or “every.” Replace it with “if” Make sense of the statement (add necessary words) Everyone who lives in Watts lives in California. All trees are green. Every teacher at Simon Tech is Canadian.

Hypothesis (p) If you live in Watts, then you live in California. If it has been raining, then the ground is wet.

Conclusion (q) If you live in Watts, then you live in California. If it has been raining, then the ground is wet.

If hypothesis, then conclusion. If p, then q.

Counterexample Proves that a conditional statement is false. Fits the hypothesis but not the conclusion.

Negation The statement the counterexample fits. If p then not q. If you live in Watts, then you do not live in California.

Converse Reversing the hypothesis and conclusion. If q then p. If you live in California, then you live in Watts.

Inverse Negating the hypothesis and conclusion. If not p then not q. If you do not live in Watts, then you do not live in California.

Contrapositive Negating the hypothesis and conclusion AND reversing them. If not q then not p. If you do not live in California, then you do not live in Watts.

Biconditional The conditional and the converse combined If p then q AND if q then p. P if and only if q. P iff q. You live in California if and only if you live in Watts.

On your notecard… Write a conditional statement. (in If-then form)

Practice

Today’s Objectives Use counterexamples to disprove conditional statements. Explain the relationship between hypothesis and conclusion. Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. Use Problem Solving Skills

Exit slip 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.” 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.) 3. If I receive a scholarship, I will go to college. A. Write the negation. B. Write the converse. C. Write the inverse. D. Write the contrapositive. 4. Write a statement that you are a counterexample to.

DO NOW Take a blank notecard from the front bookshelf (for later). In your notebook, explain why the following statements are false. If you live in California, you live in Watts If the ground is wet, then it has been raining.

Introduction to Logic Logic and Reasoning

Today’s Objectives Use counterexamples to disprove conditional statements. Explain the relationship between hypothesis and conclusion. Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. Use Problem Solving Skills

Conditional Statement An if-then statement Symbolized by p –> q Which p is a hypothesis and q is a conclusion.

Making a statement conditional. Get rid of the word “all” or “every.” Replace it with “if” Make sense of the statement (add necessary words) Everyone who lives in Watts lives in California. All trees are green. Every teacher at Simon Tech is Canadian.

Hypothesis (p) If you live in Watts, then you live in California. If it has been raining, then the ground is wet.

Conclusion (q) If you live in Watts, then you live in California. If it has been raining, then the ground is wet.

If hypothesis, then conclusion. If p, then q.

Counterexample Proves that a conditional statement is false. Fits the hypothesis but not the conclusion.

Negation The statement the counterexample fits. If p then not q. If you live in Watts, then you do not live in California.

Converse Reversing the hypothesis and conclusion. If q then p. If you live in California, then you live in Watts.

Inverse Negating the hypothesis and conclusion. If not p then not q. If you do not live in Watts, then you do not live in California.

Contrapositive Negating the hypothesis and conclusion AND reversing them. If not q then not p. If you do not live in California, then you do not live in Watts.

Biconditional The conditional and the converse combined If p then q AND if q then p. P if and only if q. P iff q. You live in California if and only if you live in Watts.

On your notecard… Write a conditional statement. (in If-then form)

Practice

Today’s Objectives Use counterexamples to disprove conditional statements. Explain the relationship between hypothesis and conclusion. Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. Use Problem Solving Skills

Exit slip 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.” 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.) 3. If I receive a scholarship, I will go to college. A. Write the negation. B. Write the converse. C. Write the inverse. D. Write the contrapositive. 4. Write a statement that you are a counterexample to.

DO NOW Take a blank notecard from the front bookshelf (for later). In your notebook, explain why the following statements are false. If you live in California, you live in Watts If the ground is wet, then it has been raining.

Error Analysis Compare your exit slip to this example.

Introduction to Logic Logic and Reasoning

Today’s Objectives Use counterexamples to disprove conditional statements. Explain the relationship between hypothesis and conclusion. Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. Use Problem Solving Skills

Conditional Statement An if-then statement Symbolized by p –> q Which p is a hypothesis and q is a conclusion.

Making a statement conditional. Get rid of the word “all” or “every.” Replace it with “if” Make sense of the statement (add necessary words) Everyone who lives in Watts lives in California. All trees are green. Every teacher at Simon Tech is Canadian.

Hypothesis (p) If you live in Watts, then you live in California. If it has been raining, then the ground is wet.

Conclusion (q) If you live in Watts, then you live in California. If it has been raining, then the ground is wet.

If hypothesis, then conclusion. If p, then q.

Counterexample Proves that a conditional statement is false. Fits the hypothesis but not the conclusion.

Negation The statement the counterexample fits. If p then not q. If you live in Watts, then you do not live in California.

Converse Reversing the hypothesis and conclusion. If q then p. If you live in California, then you live in Watts.

Inverse Negating the hypothesis and conclusion. If not p then not q. If you do not live in Watts, then you do not live in California.

Contrapositive Negating the hypothesis and conclusion AND reversing them. If not q then not p. If you do not live in California, then you do not live in Watts.

Biconditional The conditional and the converse combined If p then q AND if q then p. P if and only if q. P iff q. You live in California if and only if you live in Watts.

On your notecard… Write a conditional statement. (in If-then form)

Practice

Today’s Objectives Use counterexamples to disprove conditional statements. Explain the relationship between hypothesis and conclusion. Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. Use Problem Solving Skills

Exit slip 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.” 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.) 3. If I receive a scholarship, I will go to college. A. Write the negation. B. Write the converse. C. Write the inverse. D. Write the contrapositive. 4. Write a statement that you are a counterexample to.

DO NOW Take a blank notecard from the front bookshelf (for later). In your notebook, explain why the following statements are false. If you live in California, you live in Watts If the ground is wet, then it has been raining.

Error Analysis Compare your exit slip to this example.

Introduction to Logic Logic and Reasoning

Today’s Objectives Use counterexamples to disprove conditional statements. Explain the relationship between hypothesis and conclusion. Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. Use Problem Solving Skills

Conditional Statement An if-then statement Symbolized by p –> q Which p is a hypothesis and q is a conclusion.

Making a statement conditional. Get rid of the word “all” or “every.” Replace it with “if” Make sense of the statement (add necessary words) Everyone who lives in Watts lives in California. All trees are green. Every teacher at Simon Tech is Canadian.

Hypothesis (p) If you live in Watts, then you live in California. If it has been raining, then the ground is wet.

Conclusion (q) If you live in Watts, then you live in California. If it has been raining, then the ground is wet.

If hypothesis, then conclusion. If p, then q.

Counterexample Proves that a conditional statement is false. Fits the hypothesis but not the conclusion.

Negation The statement the counterexample fits. If p then not q. If you live in Watts, then you do not live in California.

Converse Reversing the hypothesis and conclusion. If q then p. If you live in California, then you live in Watts.

Inverse Negating the hypothesis and conclusion. If not p then not q. If you do not live in Watts, then you do not live in California.

Contrapositive Negating the hypothesis and conclusion AND reversing them. If not q then not p. If you do not live in California, then you do not live in Watts.

Biconditional The conditional and the converse combined If p then q AND if q then p. P if and only if q. P iff q. You live in California if and only if you live in Watts.

On your notecard… Write a conditional statement. (in If-then form)

Practice

Today’s Objectives Use counterexamples to disprove conditional statements. Explain the relationship between hypothesis and conclusion. Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. Use Problem Solving Skills

Exit slip 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.” 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.) 3. If I receive a scholarship, I will go to college. A. Write the negation. B. Write the converse. C. Write the inverse. D. Write the contrapositive. 4. Write a statement that you are a counterexample to.

DO NOW Take a blank notecard from the front bookshelf (for later). In your notebook, explain why the following statements are false. If you live in California, you live in Watts If the ground is wet, then it has been raining.

Error Analysis Compare your exit slip to this example.

Introduction to Logic Logic and Reasoning

Today’s Objectives Use counterexamples to disprove conditional statements. Explain the relationship between hypothesis and conclusion. Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. Use Problem Solving Skills

Conditional Statement An if-then statement Symbolized by p –> q Which p is a hypothesis and q is a conclusion.

Making a statement conditional. Get rid of the word “all” or “every.” Replace it with “if” Make sense of the statement (add necessary words) Everyone who lives in Watts lives in California. All trees are green. Every teacher at Simon Tech is Canadian.

Hypothesis (p) If you live in Watts, then you live in California. If it has been raining, then the ground is wet.

Conclusion (q) If you live in Watts, then you live in California. If it has been raining, then the ground is wet.

If hypothesis, then conclusion. If p, then q.

Counterexample Proves that a conditional statement is false. Fits the hypothesis but not the conclusion.

Negation The statement the counterexample fits. If p then not q. If you live in Watts, then you do not live in California.

Converse Reversing the hypothesis and conclusion. If q then p. If you live in California, then you live in Watts.

Inverse Negating the hypothesis and conclusion. If not p then not q. If you do not live in Watts, then you do not live in California.

Contrapositive Negating the hypothesis and conclusion AND reversing them. If not q then not p. If you do not live in California, then you do not live in Watts.

Biconditional The conditional and the converse combined If p then q AND if q then p. P if and only if q. P iff q. You live in California if and only if you live in Watts.

On your notecard… Write a conditional statement. (in If-then form)

Practice

Today’s Objectives Use counterexamples to disprove conditional statements. Explain the relationship between hypothesis and conclusion. Find the converse, inverse, contrapositive, and biconditional statements from a conditional statement. Use Problem Solving Skills

Exit slip 1. Give a counterexample to the statement “If you are a student at Simon Tech, you live in Watts.” 2. Explain the relationship between the hypothesis and conclusion. (You may use the statement in #1 or #3 if you would like.) 3. If I receive a scholarship, I will go to college. A. Write the negation. B. Write the converse. C. Write the inverse. D. Write the contrapositive. 4. Write a statement that you are a counterexample to.