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You can put this solution on YOUR website!
i never did one like this before.
\n" ); document.write( "those instructors just get more inventive every year.
\n" ); document.write( "i think you need to use a truth table to determine the validity of this argument.
\n" ); document.write( "i read this as:
\n" ); document.write( "if (SvB) is true AND if (B->D) is true AND if (S->G) is true, THEN DvG is true.
\n" ); document.write( "this is equivalent to the statement:
\n" ); document.write( "(SvB) AND (B->D) AND (S->G) -> (DvG)
\n" ); document.write( "my truth table concerning this relationship is shown below:
\n" ); document.write( "
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\n" ); document.write( "in this table, T is true and . is false.
\n" ); document.write( "i used . rather than F because the difference between T and . shows up easier than the difference between T and F.
\n" ); document.write( "The first 4 columns are the truth tables for S, B,D,and G by themselves in relationship to each other.
\n" ); document.write( "Since there are 4 variable involved, there are 2^4 = 16 number of entries required.
\n" ); document.write( "the next column is SvB which translates to S or B.
\n" ); document.write( "S or B is true if S is true or if B is true.
\n" ); document.write( "it is only false if both S and B are false.
\n" ); document.write( "the next column is B->D which translates to B implies D, or: if B then D.
\n" ); document.write( "B implies D is true if B is true and D is true, or if B is false.
\n" ); document.write( "it is only false if B is true and D is false.
\n" ); document.write( "the next column is S->G which translates to S implies G, or: if S then G.
\n" ); document.write( "S implies G is true if S is true and G is true, or if S is false.
\n" ); document.write( "it is only false if S is true and G is false.
\n" ); document.write( "the next column is DvG which translates to D or G.
\n" ); document.write( "D or G is true if D is true or if G is true.
\n" ); document.write( "it is only false if both D and G are false.
\n" ); document.write( "the next column is (SvB)+(B->D)+S->G) which translates to SvB AND B->D AND S->G
\n" ); document.write( "it is only true if SvB and B->D and S->G are all true.
\n" ); document.write( "if any of them is false, then this category is also false.
\n" ); document.write( "the last column is ((SvB)+(B->D)+(S->G))->(DvG).
\n" ); document.write( "this says that is SvB is true and B->D is true and S->G is true, then DvG is true.
\n" ); document.write( "this last column is false only if SvB is true and B->D is true and S->G is true and DvG is false.
\n" ); document.write( "otherwise it is true.
\n" ); document.write( "since this last column is true in all circumstances, then it is reasonable to conclude that the fact that SvB and B->D and S->G are true implies that DvG is true.
\n" ); document.write( "There are no conditions where all 3 of them are true and DvG is not true.
\n" ); document.write( "i believe this is what you are looking for.
\n" ); document.write( "under the assumptions that i made about what the problem is addressing, the logic in the truth table proves that the original statements are true based on that interpretation.
\n" ); document.write( "good luck with this one.
\n" ); document.write( "hopefully this interpretation is correct.
\n" ); document.write( " \n" ); document.write( "