BICONDITIONALSBICONDITIONALS

What is a What is a biconditional?biconditional? Symbolically: (pSymbolically: (p→q) ^ (q →p)→q) ^ (q →p)

The biconditional is the conjunction of The biconditional is the conjunction of a conditional and its converse.a conditional and its converse.

p↔q : “p↔q : “p if and only if q”p if and only if q”

Here’s the Here’s the important stuff:important stuff:

Any good definition Any good definition can be written as can be written as a biconditional!a biconditional!

Truth Value of Truth Value of BiconditionalsBiconditionalsComplete the following truth table:Complete the following truth table:

pp qq pp→q→q q →pq →p (p(p→q) ^(q →p)→q) ^(q →p)

So…So…

Biconditionals are true when both Biconditionals are true when both simple sentences have the same simple sentences have the same truth value.truth value.

TT↔T results in a TRUE statement.↔T results in a TRUE statement. F↔F results in a TRUE statement.F↔F results in a TRUE statement.

Assess the statement.Assess the statement.

A candy is an M&M if and only if it A candy is an M&M if and only if it melts in your mouth and not in melts in your mouth and not in your hand.your hand.

Is this a true statement? Is this a true statement?

Is this slogan a good definition for Is this slogan a good definition for an M&M?an M&M?

Your assignment.Your assignment.

1. Use the internet to help you find 1. Use the internet to help you find 3 slogans of products that can be 3 slogans of products that can be something tested by high school something tested by high school students. (candy, appliances, students. (candy, appliances, paper towels…)paper towels…)

2. Write each of the three slogans 2. Write each of the three slogans in biconditional form.in biconditional form.

Your assignment:Your assignment:

2. Come in tomorrow with your 2. Come in tomorrow with your slogans.slogans.

3. Your group will choose 1 slogan to 3. Your group will choose 1 slogan to work with. Determine whether or work with. Determine whether or not the slogan is a good not the slogan is a good description of the product.description of the product.

Your assignmentYour assignment

4. Your group’s task is to create a 4. Your group’s task is to create a slogan that is a true reflection (by slogan that is a true reflection (by the standards of a biconditional the standards of a biconditional statement.) of that product. This statement.) of that product. This is due on is due on Thursday September Thursday September 2222ndnd..

5. By 5. By Monday, September 26Monday, September 26thth, your , your group must be able to present your new group must be able to present your new advertising campaign for the chosen advertising campaign for the chosen product.product.

It may take the following forms: It may take the following forms:

*1 – 1.5 minute *1 – 1.5 minute commercialcommercial

* 5 minute * 5 minute sales pitchsales pitch with a with a

“ “billboard” ad (on posterboard)billboard” ad (on posterboard)

* A * A print campaignprint campaign with a magazine with a magazine

advertisement (8.5 x 11) and aadvertisement (8.5 x 11) and a

billboard ad (posterboard).billboard ad (posterboard).

How will this be How will this be graded?graded? On Wednesday On Wednesday September 21September 21stst, ,

you will receive a rubric (a you will receive a rubric (a grading check sheet) that will grading check sheet) that will describe in detail how this describe in detail how this assignment will be graded.assignment will be graded.

When will we be able When will we be able to work on this?to work on this? You will have the next two class days You will have the next two class days

to work as a group on developing your to work as a group on developing your new slogan, as well as planning out new slogan, as well as planning out your new Advertising Campaign.your new Advertising Campaign.

You may also work with each other You may also work with each other after school, over the weekend in after school, over the weekend in person or by using some kind of person or by using some kind of technology chat like Skype. technology chat like Skype.