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More on Conditionals

Learn to write, rewrite, and evaluate converse, inverse, and contrapositive conditional statements. Enhance your logical reasoning skills with biconditionals and truth tables.

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More on Conditionals

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  1. More on Conditionals

  2. Objectives • Write the converse, inverse, and contrapositive of a given conditional statement. • Determine the premise and conclusion of a given conditional statement. • Rewrite a given conditional statement in standard “if . . ., then . . . form. • Rewrite a biconditional as the conjunction of two conditionals.

  3. Objectives • Determine if two statements are equivalent using truth tables. • Write an equivalent variation of a given conditional.

  4. Vocabulary • converse • inverse • contrapositive • only if • biconditional

  5. Conditionals

  6. Using the statements below, write the sentence representation of each of the symbolic expressions : p: I am a multimillion-dollar lottery winner. q: I am a world traveler.

  7. Using the statements below, write the sentence representation of each of the symbolic expressions : p: I am a multimillion-dollar lottery winner. q: I am a world traveler.

  8. Using the statements below, write the sentence representation of each of the symbolic expressions : p: I am a multimillion-dollar lottery winner. q: I am a world traveler.

  9. Using the statements below, write the sentence representation of each of the symbolic expressions : p: I am a multimillion-dollar lottery winner. q: I am a world traveler.

  10. Write the converse, inverse, and contrapositive of the sentence: If you do not eat meat, you are a vegetarian Converse: If you are a vegetarian, then you do not eat meat. Inverse: If you do eat meat, then you are not a vegetarian. Contrapositive: If you are not a vegetarian, then you do eat meat.

  11. Write the converse, inverse, and contrapositive of the sentence: You do not win, if you do not buy a lottery ticket. Converse: If you do not win, then you do not buy a lottery ticket. Inverse: If you buy a lottery ticket, then you win. Contrapositive: If you win, then you buy a lottery ticket.

  12. Determine the premise and conclusion of the statement: premise conclusion I eat raw fish only if I am in a Japanese restaurant. Rewrite the compound statement in standard form.

  13. Write the biconditional as a conjunction of two conditionals: We eat at Burger World if an only if Ju Ju’s Kitsch-Inn is closed.

  14. Translate the two statements into symbolic form and use truth tables to determine whether the statements are equivalent. • If I do not have health insurance, I cannot have surgery. • If I can have surgery, then I do have health insurance.

  15. Determine which pairs of statements are equivalent. • If Proposition III passes, freeways are improved. • If Proposition III is defeated, freeways are not improved. • If the freeways are not improved, then Proposition III does not pass. • If the freeways are improved, Proposition III passes.

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