Transcript More on Conditionals

More on Conditionals
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.
Objectives
• Determine if two statements are
equivalent using truth tables.
• Write an equivalent variation of a given
conditional.
Vocabulary
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converse
inverse
contrapositive
only if
biconditional
Conditionals
Name
Conditional
Converse
Inverse
Contrapositive
Symbolic Form
p q
q p
~ p ~ q
~ q ~ p
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.
p q
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.
q p
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.
~ p ~ q
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.
~ q ~ p
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.
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.
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.
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.
Translate the two statements
into symbolic form and use truth
tables to determine whether the
statements are equivalent.
1. If I do not have health insurance, I
cannot have surgery.
2.If I can have surgery, then I do have
health insurance.
Determine which pairs of
statements are equivalent.
1. If Proposition III passes, freeways are
improved.
2.If Proposition III is defeated,
freeways are not improved.
3.If the freeways are not improved, then
Proposition III does not pass.
4.If the freeways are improved,
Proposition III passes.