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Conditional Statements and Logic

Conditional Statements and Logic. 2.2 Ms. Verdino. Conditional Statement. A conditional statement is a statement that can be written in if-then form. “ If _____________, then ______________.”. If the batteries are dead , then then the TV remote won't work .

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Conditional Statements and Logic

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  1. Conditional Statements and Logic 2.2 Ms. Verdino

  2. Conditional Statement A conditional statement is a statement that can be written in if-then form. “If _____________, then ______________.” Ifthe batteries are dead, then then the TV remote won't work.

  3. Conditional Statements have two parts: The hypothesis is the part of a conditional statement that follows “if” (when written in if-then form.) The hypothesis is the given information, or the condition. The conclusionis the part of an if-then statement that follows “then” (when written in if-then form.) The conclusion is the result of the given information.

  4. Symbolic Logic Symbols can be used to modify or connect statements. Symbols for Hypothesis and Conclusion: Hypothesis is represented by “p”. Conclusion is represented by “q”. if p, then q or p implies q

  5. Symbolic Logic if p, then q or p implies q p  q is used to represent Example: p: a number is prime q: a number has exactly two divisors pq: If a number is prime, then it has exactly two divisors.

  6. Writing A Conditional Statement Conditional statements can be written in “if-then” form to emphasize which part is the hypothesis and which is the conclusion. Hint: Turn the subject into the hypothesis. Example 1: Vertical angles are congruent. can be written as... Conditional Statement: If two angles are vertical, then they are congruent. Example 2: can be written as... Seals swim. Conditional Statement: If an animal is a seal, then it swims.

  7. If……. Then vs. Implies Another way of writing an if-then statement is using the word implies. If two angles are vertical, then they are congruent. Two angles are verticalimplies they are congruent.

  8. Conditional statements can be true or false. • A conditional statement is false only when the hypothesis is true, but the conclusion is false. • The truth value of a conditional statement is either true or false. Statement: If you live in Tennessee, then you live in Nashville. Yes !!! Is there a counterexample? Counterexample: I live in Tennessee, BUT I live in Morristown. Therefore () the statement is false.

  9. Is the conditional true or false? If a month has 28 days, then it is February. If two angles from a linear pair, then they are supplementary. If a number is divisible by 5, then it is odd.

  10. Symbolic Logic ~ is used to represent the word “not” Example 1: p: the angle is obtuse ~p: The angle is not obtuse Note: ~p means that the angle could be acute, right, or straight. Example 2: p: I am not happy ~p: I am happy ~p took the “not” out- it would have been a double negative (not not)

  11. Symbolic Logic  is used to represent the word “therefore” Example: Therefore, the statement is false.  the statement is false

  12. Forms of Conditional Statements Converse: Switch the hypothesis and conclusion (q  p) pqIftwo angles are vertical, thenthey are congruent. qpIftwo angles are congruent, thenthey are vertical.

  13. Forms of Conditional Statements Inverse:State the opposite of both the hypothesis and conclusion. (~p~q) pq :Iftwo angles are vertical, thenthey are congruent. ~p~q:Iftwo angles are not vertical, thenthey are not congruent.

  14. Forms of Conditional Statements Contrapositive: Switch the hypothesis and conclusion and state their opposites. (~ q~p) pq : Iftwo angles are vertical, thenthey are congruent. ~q~p:Iftwo angles are not congruent, thenthey are not vertical.

  15. Forms of Conditional Statements • Contrapositives are logically equivalent to the original conditional statement. • If pq is true, then qp is true. • If pq is false, then qp is false.

  16. Compound statement A compound statement combines two or more statements.

  17. Symbolic Logic  “or” is used to represent the word p: a number is even q: a number is divisible by 3 Example: pq: A number is even or it is divisible by 3. i.e.2,3,4,6,8,9,10,12,14,15,...

  18. Symbolic Logic  is used to represent the word “and” p:a number is even q: a number is divisible by 3 Example: A number is even and it is divisible by 3. i.e. 6,12,18,24,30,36,42... pq:

  19. Constructing a compound statement s: We will go to the beach j: We will go out to dinner t: We will go to the movies sjsj s(jt) (sj) t

  20. Truth tables

  21. Creating a truth table

  22. Biconditional Statements • When a conditional statement and its converse are both true, the two statements may be combined. • Use the phrase if and only if (sometimes abbreviated: iff) Statement: If an angle is right then it has a measure of 90. Converse:If an angle measures 90, then it is a right angle. Biconditional:An angle is right if and only if it measures 90.

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