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I am having a lot of trouble with word problem questions. If someone could help me that would be great. If you could show your work so that I can understand how you got the answer would be apprectiated. Thanks so much!
\n" ); document.write( "4. (4 pts) For each of the following conditionals, identify the antecedent and the consequent. Form the converse, inverse, and contrapositive.
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document.write( "You need to memorize this for the conditional:\r\n" );
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document.write( "When you have \"IF p THEN q\" \r\n" );
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document.write( "1. \"IF p THEN q\" is written as \"p -> q\"\r\n" );
document.write( "2. p, the object of \"IF\", is the antecedent and the q, the object of \r\n" );
document.write( "\"THEN\", is the consequence.\r\n" );
document.write( "3. The converse of p -> q is gotten by reversing the antecedent and \r\n" );
document.write( "the consequence and getting q -> p\r\n" );
document.write( "4. The inverse of p -> q is gotten by negating the antecedent and \r\n" );
document.write( "the consequence and getting ~p -> ~q.\r\n" );
document.write( "4. The contrapositive of p -> q is gotten by both reversing the \r\n" );
document.write( "antecedent and the consequence and negating them ~q -> ~p\r\n" );
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document.write( "Remember this:\r\n" );
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document.write( "\"IF ANTECEDENT, THEN CONSEQUENCE\"{ \r\n" );
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document.write( "(a) If I don’t go to the movie, I’ll study my math. \r\n" );
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document.write( "Always look for an IF and a THEN, even when they are only understood.\r\n" );
document.write( "Here the THEN is understood:\r\n" );
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document.write( "IF I don’t go to the movie, THEN I’ll study my math.\r\n" );
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document.write( "Here p = \"I don't go to the movie\" = the antecedent\r\n" );
document.write( " q = \"I'll study my math\" = the consequence\r\n" );
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document.write( "and the statement is p -> q\r\n" );
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document.write( "CONVERSE: q -> p (switch them but don't negate them)\r\n" );
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document.write( "If I’ll study my math, then I don’t go to the movie.\r\n" );
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document.write( "Now we know what that means, but people don't talk like that,\r\n" );
document.write( "so we have to re-write it by changing the tenses of the verbs, say, as:\r\n" );
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document.write( "If I end up having studied my math, then I won’t have gone to the movie.\r\n" );
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document.write( "INVERSE: ~p -> ~q (negate them but don't switch them\")\r\n" );
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document.write( "If I’ll NOT study my math, then I don’t NOT go to the movie.\r\n" );
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document.write( "Again, we know what that means, but, as we said before, people don't \r\n" );
document.write( "talk like that, so we have to re-write it by changing the tenses of the \r\n" );
document.write( "verbs, and removing the double negative \"don't NOT\" \r\n" );
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document.write( "If I do NOT study my math, then I will go to the movie.\r\n" );
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document.write( "CONTRAPOSITIVE: ~q -> ~p (negate them and switch them)\r\n" );
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document.write( "If I NOT study my math, then I don’t NOT go to the movie.\r\n" );
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document.write( "We know what that means, but people don't talk like that,\r\n" );
document.write( "so we have to re-write it, say, as:\r\n" );
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document.write( "If I don't study my math, then I will go to the movie.\r\n" );
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document.write( "(b) Your car won’t start if you don’t have gasoline in the tank. \r\n" );
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document.write( "This one you have to rewrite the original with the IF clause FIRST:\r\n" );
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document.write( "IF you don’t have gasoline in the tank, THEN your car won't start.\r\n" );
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document.write( "So the antecedent is \"you don’t have gasoline in the tank\" and\r\n" );
document.write( "the consequence is \"your car won't start\".\r\n" );
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document.write( "To get the converse, just switch them:\r\n" );
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document.write( "IF your car won't start THEN you don’t have gasoline in the tank.\r\n" );
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document.write( "To get the inverse just negate them only.\r\n" );
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document.write( "IF you don’t NOT have gasoline in the tank, THEN your car won't NOT start. \r\n" );
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document.write( "Now get rid of the double negatives \"don't NOT\" and \"wont NOT\":\r\n" );
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document.write( "IF you have gasoline in the tank, THEN your car will start.\r\n" );
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document.write( "To get the contrapositive, switch them and also negate them:\r\n" );
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document.write( "IF your car won't NOT start THEN you don’t NOT have gasoline in the tank.\r\n" );
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document.write( "Now get rid of the double negatives:\r\n" );
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document.write( "IF your car will start THEN you do have gasoline in the tank.\r\n" );
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document.write( "Edwin \n" );
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