document.write( "Question 476261: If the argument below is valid, name which of the four valid forms of argument is represented. If it is not valid, name the fallacy that is represented.
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\n" ); document.write( "If the water is filtered, then it does not contain lead.
\n" ); document.write( "The water does not contain lead.
\n" ); document.write( "Therefore, the water is filtered. \n" ); document.write( "

Algebra.Com's Answer #326598 by Theo(13342) $\"\"$ $\"About$

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if the water is filtered, then it does not contain lead.
\n" ); document.write( "the water does not contain lead.
\n" ); document.write( "therefore, the water is filtered.
\n" ); document.write( "-----
\n" ); document.write( "this argument is not valid.
\n" ); document.write( "if is not valid by the fallacy of the .....
\n" ); document.write( "here's a reference that contains all the valid argument types and the fallacy types.
\n" ); document.write( "http://ux.brookdalecc.edu/fac/tlt/math/136/logic.pdf
\n" ); document.write( "your answer is on page 7 of this document.
\n" ); document.write( "it's called \"fallacy of the converse\"
\n" ); document.write( "the symbolic form would be:
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document.write( "premise 1:        p->q\r\n" );
document.write( "premise 2:        q\r\n" );
document.write( "conclusion:       therefore p\r\n" );
document.write( "

\n" ); document.write( "to understand why this is a fallacy, you need to go to the truth tables for the implies statement.
\n" ); document.write( "that truth table is shown below:
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\n" ); document.write( " p q p->q
\n" ); document.write( " T T T
\n" ); document.write( " T F F
\n" ); document.write( " F T T
\n" ); document.write( " F F T
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\n" ); document.write( "you can see from this table that the only time q if false is when p is true and q is false.
\n" ); document.write( "if p is false, then q can be true or false and the statment is still true.
\n" ); document.write( "the fallacy of the converse states that the following logic is invalid.
\n" ); document.write( "p->q
\n" ); document.write( "q
\n" ); document.write( "therefore p
\n" ); document.write( "it is saying that because q is true, then p must be true.
\n" ); document.write( "but you can see from the truth table for the implied statement that when q is true, p can either be false or true, therefore, you can't make that statement shown in the fallacy of the converse.
\n" ); document.write( "just because p implies q doesn't mean that q implies p.
\n" ); document.write( "the converse of a statement is shown below in symbolic form.
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document.write( "statement:    p->q\r\n" );
document.write( "converse:     q->p\r\n" );
document.write( "

\n" ); document.write( "this can be true some of the time and can be false some of the time. it is not always true.
\n" ); document.write( "an example of when it is not true would be:
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document.write( "statement:     all cats are mammals\r\n" );
document.write( "converse:      all mammals are cats\r\n" );
document.write( "

\n" ); document.write( "while the statement is true, its converse is clearly not true.
\n" ); document.write( "that's why your problem statement is invalid by the fallacy of the converse.
\n" ); document.write( "your statement:
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document.write( "statement:     if the water is filtered, it does not contain lead.\r\n" );
document.write( "converse:      if the water does not contain lead, it is filtered.\r\n" );
document.write( "

\n" ); document.write( "nowhere in the statement does it implied the converse is true.
\n" ); document.write( "if the water does not contain lead, it may or may not be filtered.
\n" ); document.write( "not all water contains lead.
\n" ); document.write( " \n" ); document.write( "

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