Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then”...

10
Unit 2: Proofs

Transcript of Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then”...

Page 1: Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then” statement. Example: If a car is a Wrangler, then it is a.

Unit 2: Proofs

Page 2: Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then” statement. Example: If a car is a Wrangler, then it is a.

Conditional Statements• Conditional statement is the mathy term for “if-then” statement.

• Example: If a car is a Wrangler, then it is a Jeep.• In a conditional, the part following the word “if” is the hypothesis.

• Hypothesis: a car is a Wrangler• ** Leave the “If” off **

• The part following the word “then” is the conclusion.• Conclusion: it is a Jeep• ** Leave the “then” off **

• In logical notation, conditionals are written as follows:If p, then q or p => q (which reads as “p implies q.”)

Page 3: Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then” statement. Example: If a car is a Wrangler, then it is a.

Euler (pronounced “Oiler”) DiagramsCreate a Euler diagram for the previous conditional:

“If a car is a Wrangler, then it is a Jeep.”

Page 4: Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then” statement. Example: If a car is a Wrangler, then it is a.

More Euler• Consider the following statement: Timmy’s car is a Wrangler.• Where should we place Timmy’s car in the diagram?

• By placing Timmy’s car into the Wrangler category on the Euler diagram, you can see that it is also included in the Jeep category.

Page 5: Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then” statement. Example: If a car is a Wrangler, then it is a.

Now let’s write it using words…

Logical Argument:1. If a car is a Wrangler, then it is a Jeep.2. Timmy’s car is a Wrangler.3. Therefore, Timmy’s car is a Jeep.

This process is known as deductive reasoning, or deduction.

Page 6: Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then” statement. Example: If a car is a Wrangler, then it is a.

Example

1. Draw a Euler diagram that conveys the following information:If a student has Mr. Brilliandt for English, then they are student at GMC. Susan has Mr. Brilliandt for English.

2. What conclusion can you draw about Susan?

Page 7: Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then” statement. Example: If a car is a Wrangler, then it is a.

Reversing Conditionals• When you interchange the hypothesis and the conclusion of a

conditional, the new conditional is called the converse of the original.• Example: Conditional: If a car is a Civic, then it is a Honda.

Converse: If a car is a Honda, then it is a Civic.• The original conditional statement is true!• Is the converse?• Is there an example of a Honda that is not a Civic?

• If so, then the converse is false!• An example that proves a statement is false is called a counterexample.• What is a counterexample for the given converse?

Page 8: Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then” statement. Example: If a car is a Wrangler, then it is a.

Practice1. Write a conditional with the hypothesis “the polygon has

four congruent sides” and the conclusion “the polygon is a square.”

2. Write the converse.

3. Is the conditional true? If no, what is a counterexample?

4. Is the converse true? If no, what is a counterexample?

If the polygon has 4 congruent sides, then the polygon is a square.

If the polygon is a square, then the polygon has 4 congruent sides.

No, counterexample: rhombus

YES!!

Page 9: Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then” statement. Example: If a car is a Wrangler, then it is a.

Logical Chains• Conditionals that can be linked together are called logical chains.• Consider the following silly conditionals:

If cats freak, then mice RUN.If sirens shriek, then dogs howl.If dogs howl, then cats freak.

• Prove that the following conditional follows logically from the three given conditionals:

If sirens shriek, then mice RUN.

Hypothesis:

1.

2.

3.

Page 10: Unit 2: Proofs. Conditional Statements Conditional statement is the mathy term for “if-then” statement. Example: If a car is a Wrangler, then it is a.

If-Then Transitive PropertyGiven: You can conclude:If A then B, and if B then C If A then C.

Example:Given:

If there is a parade, then fireworks will go off.If it is July 4, then flags are flying.If flags are flying, then there is a parade.

Prove: If it is July 4, then fireworks go off.Hypothesis:1.

2.

3.


Conditional Statement Chapter 8. Conditional Statements Are statements that check an expression then may or may not execute a statement or group of statement.

Conditional Statement Chapter 8. Conditional Statements Are statements that check an expression then may or may not execute a statement or group of statement.

Nested conditional statements. Previously discussed Conditional statements discussed so far: Syntax of the if-statement: if-statement if-else-statement.

Nested conditional statements. Previously discussed Conditional statements discussed so far: Syntax of the if-statement: if-statement if-else-statement.

2.2 Write Definitions as Conditional Statements. Conditional Statement A logical statement with a hypothesis and a conclusion. If-then form: “If” part.

2.2 Write Definitions as Conditional Statements. Conditional Statement A logical statement with a hypothesis and a conclusion. If-then form: “If” part.

Conditional statement in java

Conditional statement in java

Conditional statement ss2

Conditional statement ss2

Assigning value Conditional statement LoopsExamplescompalg.inf.elte.hu/~czirbusz/teaching/compalgsys/FundamentalsOf... · Assigning value Conditional statement LoopsExamples Index

Assigning value Conditional statement LoopsExamplescompalg.inf.elte.hu/~czirbusz/teaching/compalgsys/FundamentalsOf... · Assigning value Conditional statement LoopsExamples Index

Conditional Statement A conditional statement has two parts, a hypothesis and a conclusion. When conditional statements are written in if-then form, the.

Conditional Statement A conditional statement has two parts, a hypothesis and a conclusion. When conditional statements are written in if-then form, the.

2.1 Conditional Statements - Weeblyederushe.weebly.com/uploads/3/7/6/5/37655305/geo_2.1.pdfSection 2.1 Conditional Statements 65 2.1 Conditional Statements Determining Whether a Statement

2.1 Conditional Statements - Weeblyederushe.weebly.com/uploads/3/7/6/5/37655305/geo_2.1.pdfSection 2.1 Conditional Statements 65 2.1 Conditional Statements Determining Whether a Statement

Conditional Statement in C Language

Conditional Statement in C Language

 · Every conditional statement has three related conditional statements. Geometry (H) ... 11. Write three separate conditional statements that the Venn diagram illustrates.

 · Every conditional statement has three related conditional statements. Geometry (H) ... 11. Write three separate conditional statements that the Venn diagram illustrates.

Nested conditional statements. A conditional statement (i.e., an if-statement or an if-else- statement) is also a statement We can use an if-statement.

Nested conditional statements. A conditional statement (i.e., an if-statement or an if-else- statement) is also a statement We can use an if-statement.

Nopol: Automatic Repair of Conditional Statement Bugs in ... · Nopol: Automatic Repair of Conditional ... Automatic Repair of Conditional Statement Bugs in Java ... This extension

Nopol: Automatic Repair of Conditional Statement Bugs in ... · Nopol: Automatic Repair of Conditional ... Automatic Repair of Conditional Statement Bugs in Java ... This extension

MGCUB, INDIA Conditional Statement-I · 2020. 4. 29. · M3 Conditional Statement-I Mr. J. Mishra MGCUB, INDIA Objectives Introduction if Statement Multiple if Statement if …else

MGCUB, INDIA Conditional Statement-I · 2020. 4. 29. · M3 Conditional Statement-I Mr. J. Mishra MGCUB, INDIA Objectives Introduction if Statement Multiple if Statement if …else

Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form.

Lesson 2.1 Conditional Statements. Conditional Statement Two parts: hypothesis and conclusion If-then form.

2.1 Conditional Statements Conditional Statement – a logical statement with two parts. P, the “if part”, hypothesis Q, the “then part”, conclusion If.

2.1 Conditional Statements Conditional Statement – a logical statement with two parts. P, the “if part”, hypothesis Q, the “then part”, conclusion If.

Conditional Statement & Loops

Conditional Statement & Loops

Part 2 Module 2 The Conditional Statement

Part 2 Module 2 The Conditional Statement

Geometry: 2.1-2.3 Notes · 2 Conditional Statement A conditional statement is a logical statement that has two parts, a hypothesis p and a conclusion q. When a conditional statement

Geometry: 2.1-2.3 Notes · 2 Conditional Statement A conditional statement is a logical statement that has two parts, a hypothesis p and a conclusion q. When a conditional statement

2.2 Conditional Statements. Goals Identify statements which are conditional Identify the antecedent and consequent of a conditional statement Negate conditional.

2.2 Conditional Statements. Goals Identify statements which are conditional Identify the antecedent and consequent of a conditional statement Negate conditional.

Conditional Statement

Conditional Statement