Conditional Statements Eric Hoffman Algebra II PLHS Aug. 2007.

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Conditional Statements Eric Hoffman Algebra II PLHS Aug. 2007

Bell Problems Make a conjecture as to how many rows need to be put in your truth tables –Note: a conjecture is an educated guess based off of known knowledge For example: a compound statement with 2 statements needs 4 rows a compound statement with 3 statements needs 8 rows How many rows will be needed for the truth table containing 4 statements?? 5 statemens??

Key Topics Conditional Statement : a statement that can be written in “if, then” form –Ex. If you study for your test, then you will do well If-then statement: an if-then statement is written in the form “if p then q” – p → q, read as “if p then q” or “p implies q” Statement immediately following the “if ” is called the hypothesis Statement immediately following the “then” is called the conclusion

Key Topics Truth Table for an “if-then” statement Important: Notice the statement is always true unless the hypothesis is true and the conclusion is false

Practice Using Prior Knowledge On your white-boards make a truth table for the following statements: 1.(pΛq) Λ (pVr) 2.(p Λ q) → r 3.(p Λ q) → (pΛq) Λ (pVr) pqrpΛqpΛqpVr(pΛq) Λ (pVr)(pΛq)→(pΛq) Λ (pVr) TTTTTTT TFTFTFT TTFTTTT TFFFTFT FTTFTFT FFTFTFT FTFFFFT FFFFFFT

Key Topics Related Conditionals : other statements based on given conditional statements Given conditional statement p→q –Converse: q→p –Contrapositive: ~q→~p –Inverse: ~p→~q

Key Topics Logically equivalent: statements that have the same truth value are said to be logically equivalent –Note: the conditional statement is logically equivalent to the contrapositive, and the converse is logically equivalent to the inverse

Key Topics

Homework: pg. 78, even