Logic Statements

Yesterday's lesson introduced the manipulations and truth value of logic statements. Much of this lesson is knowing and applying the definitions: Conditional statement, converse, inverse, and contrapositive.

The conditional statement has the "if - then" format. The "condition to be met" is called the hypothesis and follows "if". The "result" is called the conclusion and follows "then"
Example: If all students are present on the day of a quiz, then they will get 2 bonus points. (This is true for my classes.)

The converse switches the hypothesis and the conclusion.
Example: If all students get 2 bonus points, then they were all present on the day of a quiz. (This could be true, but it could be false if they all did a bonus problem correctly and that is why they got the bonus points. This is called a counterexample, it is an example that counters the argument.)

The inverse is formed by negating both the hypothesis and the conclusion of the original conditional statement.
Example: If all students are not present on the day of a quiz, then they will not get 2 bonus points. (Again, this may not be true if they still answer the bonus question for the extra points.)

The contrapositive is formed by switching and negating both the hypothesis and conclusion of the original conditional (this is a combination of the converse and the inverse).
Example: If all students did not get 2 bonus points, then they were not all present on the day of a quiz. (This is true for my classes.)

The second day of this lesson brings in the final logic statement. The biconditional statement is formed with both the conditional statement and the converse are true. It is not written in "if - then" form. Instead, this statement places "if and only if" in the middle of the hypothesis and conclusion (sometimes abbreviated "iff"). Definitions are often written in the biconditional format in our class.
Example: An angle is a right angle if and only if it measures 90 degrees (the definition of right angle).

Homework: Yesterday's - Page 207, #1 - 10 and Page 209, #1 - 8. Today's - Page 207, #11 - 19 and Page 209, #17 - 19.

Students were also given a project today. This project is called "The Logic of Advertising". Individually, or in pairs, the students must find 3 slogans to convert to conditional statements and then write the converse, inverse, and contrapositive. All 12 sentences (4 sentences for each of 3 ads) must be typed and clearly identified on a single sheet of paper. Then, a presentation can be made (power point, poster, video) to share the sentences with the class. This project is due on Friday, November 20th.

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