 Writing conditionals  Using definitions as conditional statements  Writing biconditionals  Making truth tables.

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Presentation transcript:

 Writing conditionals  Using definitions as conditional statements  Writing biconditionals  Making truth tables

 Conditional: logical statement that has a hypothesis and conclusion  If-then form: how a conditional is written  Hypothesis: if part of if-then  Conclusion: then part of if-then  Negation: opposite of original statement  Converse: statement written conclusion and then hypothesis  Inverse: negate both hypothesis and conclusion of a conditional  Contrapositive: negate the converse of a conditional  Equivalent statements: when both statements are true or false  Biconditional: phrase containing “if and only if”  Truth value: whether statement is true or false  Truth table: shows whether conditional is true or false based on hypothesis and conclusion

 Hyp – all birds, con – have feathers  If something is a bird, then it has feathers.  Hyp – you are in Texas, con – you are in Houston.  If you are in Texas, then you are in Houston.  Identify hypothesis and conclusion and write as a conditional  Statement:  All birds have feathers  You are in Texas if you are in Houston.

 Negation:  The ball is not red  The cat is black  Statement:  The ball is red  The cat is not black

 Symbolic Forms TypeWordsSymbols ConditionalIf p, then qp → q ConverseIf q, then pq → p InverseIf not p, then not q~p → ~q ContrapositiveIf not q, then not p~q → ~p Biconditionalp if and only if qp ↔ q

 Let p be “you are a guitar player” and q be “you are a musician.” Write each statement.  Conditional:  If you are a guitar player, then you are a musician.  Converse:  If you are a musician, then you are a guitar player.  Inverse:  If you are not a guitar player, then you are not a musician.  Contrapositive:  If you are not a musician, then you are not a guitar player.

 Let p be “two angles are supplementary” and let q be “the measures of the angles sum to 180.”  Write each statement  Conditional:  If two angles are supplementary, then the measures of the angles sum to 180.  Converse:  If the measures of the angles sum to 180, then the two angles are supplementary.  Inverse:  If the two angles are not supplementary, then the measures of the angles do not sum to 180.  Contrapositive:  If the measures of the angles does not sum to 180, then the two angles are not supplementary.

 Definition:  Write conditional and converse of definition and check truth value.  If true or false  If conditional and converse are true, then can write a biconditional