document.write( "Question 179325This question is from textbook
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\n" ); document.write( " If a dog is barking, then it will not bite
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Algebra.Com's Answer #134242 by Edwin McCravy(20054) $\"\"$ $\"About$

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Edwin's solution:
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\n" ); document.write( "Note: Fombitz has
\n" ); document.write( "Original Statement: if (a) then (b)
\n" ); document.write( "Converse Statement: if (a) then (b)
\n" ); document.write( "Inverse Statement: if (not a) then (not b)
\n" ); document.write( "Contrapositive Statement: if (not a) then (not b)
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\n" ); document.write( "But he should have had:
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\n" ); document.write( "Original Statement: if (a) then (b)
\n" ); document.write( "Converse Statement: if (b) then (a)
\n" ); document.write( "Inverse Statement: if (not a) then (not b)
\n" ); document.write( "Contrapositive Statement: if (not b) then (not a)
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\n" ); document.write( "Write the converse, inverse, and contrapositive of the following conditional statement
\n" ); document.write( "If a dog is barking, then it will not bite.
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document.write( "Write that as BARKING -> ~BITE\r\n" );
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document.write( "Then use the rules:\r\n" );
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document.write( "1. To form the converse conditional of a given conditional,\r\n" );
document.write( "exchange what's on the left of the -> with what's on the right.\r\n" );
document.write( "(But do not NEGATE either one.)\r\n" );
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document.write( "So the converse conditional of the given conditional\r\n" );
document.write( "BARKING -> ~BITE\r\n" );
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document.write( "is\r\n" );
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document.write( "~BITE -> BARKING, or\r\n" );
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document.write( "If a dog will not bite, then it will be barking.\r\n" );
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document.write( "Note: I changed \"is barking\" to \"will be barking\" to make\r\n" );
document.write( "the sentence clearer without changing the meaning. You can\r\n" );
document.write( "change the tense of the verbs without changing the meaning.\r\n" );
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document.write( "---\r\n" );
document.write( "2. To form the inverse conditional of a given conditional,\r\n" );
document.write( "NEGATE both what's on the left of the -> as well as what's \r\n" );
document.write( "on the right. (But do not exchange them). To NEGATE, if \r\n" );
document.write( "there is a ~ before it, take it off, and if there is no ~ \r\n" );
document.write( "before it, put a ~ before it.\r\n" );
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document.write( "So the inverse conditional of the given conditional\r\n" );
document.write( "BARK -> ~BITE\r\n" );
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document.write( "is\r\n" );
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document.write( "~BARK -> BITE, or\r\n" );
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document.write( "If a dog is not barking, then it will bite.\r\n" );
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document.write( "---\r\n" );
document.write( "3. To form the contrapositive conditional of a given conditional,\r\n" );
document.write( "EXCHANGE what's on the left of the -> with what's on the right AND\r\n" );
document.write( "NEGATE them also.\r\n" );
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document.write( "So the contrapositive conditional of the given conditional\r\n" );
document.write( "BARK -> ~BITE\r\n" );
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document.write( "is\r\n" );
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document.write( "BITE -> ~BARK, or\r\n" );
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document.write( "If a dog will bite, then it will not be barking.\r\n" );
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document.write( "---------\r\n" );
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document.write( "Notice also these facts that will help you understand: \r\n" );
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document.write( "1. the original statement and the contrapositive \r\n" );
document.write( "   are equivalent statements.\r\n" );
document.write( "2. the converse and the inverse are equivalent\r\n" );
document.write( "   statements.\r\n" );
document.write( "3. the original and its equivalent contrapositive ARE NOT\r\n" );
document.write( "   equivalent to the equivalent inverse and converse.\r\n" );
document.write( "4. the inverse is the contrapositive of the converse.\r\n" );
document.write( "5. the converse is the contrapositive of the inverse.\r\n" );
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document.write( "Edwin

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