course Mth 151 |ͺ{ۏwo{assignment #013
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22:14:01 `q001. There are 4 questions in this set. Two statements are said to be negations of one another if exactly one of the statements must be true. This means that if one statement is true the other must be false, and if one statement is false the other must be true. What statement is the negation of the statement 'all men are over six feet tall'?
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RESPONSE --> The nagation is some men are not over six feet tall. confidence assessment: 2
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22:16:06 It doesn't matter what's true and what isn't. If the question was to write the negation of 'all men are under 20 feet tall' you would still state the negation as 'some men are under 20 feet tall'. In this case the negation is true, which proves that the statement itself is false.
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RESPONSE --> all men are over six feet tall no men are over six feet tall some men are over six feet tall self critique assessment: 1
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22:16:49 In the given problem the negation 'some men are under 6 ft tall' is true, proving that the original statement 'all men are over 6 ft tall' is false.
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RESPONSE --> true self critique assessment: 1
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22:17:20 These examples demonstrate why it is important to figure out the negation before you even thing about which statement is true. Either the statement or its negation will be true, but never both.
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RESPONSE --> true self critique assessment: 2
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22:17:47 `q002. What is the negation of the statement 'some men are over six feet tall' ?
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RESPONSE --> no men are over six feet tall confidence assessment: 3
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22:22:47 `q003. As seen in the preceding two questions, the negation of a statement that says 'all are' or 'all do' is 'some aren't' or 'some don't', and the negation of a statement that says 'some are' or 'some do' is 'all aren't' or 'none are', or 'all do not' or 'none do'. Each of the following statements can be expressed as and 'all' statement or a 'some' statement. Identify which is which and give the negation of each statement: 1. Every dog has its day. 2. Some roses are black. 3. Every attempt fails. 4. In some cases the desired outcome isn't attained.
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RESPONSE --> 1Every dog has its day the negation is : All dogs do have their day 2 Some rose are balck the negation is : No roses are black 3 Every attempt fails the negation is : Some attempts do not fail 4 In some cases the desired out come is not attained. the negation is : no out comes are not as desired. confidence assessment: 2
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22:26:47 `q004. Negate the following statements: 1. No roses are black. 2. Some roses are not black. 3. There were Dodo birds that weren't stupid. 4. There were never turtles that weren't slow.
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RESPONSE --> 1. no roses are black the negation is : Some roses are not black 2. Some roses are not black the negation is : all roses are not black. 3. There were Dodo birds the weren't stupid the negation is : All Dodo birds aren't stupid 4. There were never turtles that werent slow. the negation is: All turtles are slow. confidence assessment: 2
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lݿlŕd assignment #014 014. Truth Tables Liberal Arts Mathematics I 10-29-2007
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20:00:51 `q001. There are 8 questions in this set. If each of the propositions p and q can be either true or false, what combinations of truth values are possible for the two propositions (e.g., one possibility is that p is false and q is true; list the other possibilities)?
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RESPONSE --> 1. p is T , q is T 2. p is T , q is F 3. p is F, q is T 4. p is F , q is F T stands dot True F stands for False confidence assessment: 3
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20:05:56 `q002. For each of the for possibilities TT, TF, FT and FF, what is the truth value of the compound statement p ^ q ?
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RESPONSE --> TT : p^q is T, p is T and q is T TF : p^q is F, p is F and q is F FT : p^q is T, p is F and q is T FF : p^q is F, p is F and q is F confidence assessment: 3
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20:09:03 `q003. Write the results of the preceding problem in the form of a truth table.
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RESPONSE --> p q p ^ q T T T T F F F T F F F F confidence assessment: 3
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20:11:42 `q004. For each of the possible combinations TT, TF, FT, FF, what is the truth value of the proposition p ^ ~q?
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RESPONSE --> p q ~q p^~q T T F F T F T T F T F F F F T F confidence assessment: 3
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20:14:26 `q005. Give the results of the preceding question in the form of a truth table.
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RESPONSE --> p q ~q p^~q T T F F T F T T F T F F F F T F confidence assessment: 3
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20:37:52 `q006. Give the truth table for the proposition p U q, where U stands for disjunction.
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RESPONSE --> p u q p q p u q T T T T F T F T T F F F confidence assessment: 3
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20:46:47 `q007. Reason out the truth values of the proposition ~(pU~q).
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RESPONSE --> ~ ( p u ~ q) TT : p is T, q is T, ~q is F, p u ~q is T, ~(p u~q) is F TF : p is T, q is F, ~q is T, p u ~q is T, ~(p u~q) is F FT : p is F, q is T, ~q is F, p u ~q is F, ~(p u~q) is T FF : p is F, q is F, ~q is T, p u ~q is T, ~(p u~q is F confidence assessment: 3
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20:50:33 `q008. Construct a truth table for the proposition of the preceding question.
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RESPONSE --> p q ~q p u ~q ~(p u ~q) T T F T F T F T T F F T F F T F F T T F confidence assessment: 3
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