1. [-/12 Points] DETAILS SMITHNM13 3.2.010. Construct a truth table for the given statement. ( r A s ) VNS S rAs NS ( rAS) VNS T T T T F F Need Help? Read It 2. [-/16 Points] DETAILS SMITHNM13 3.2.013. Construct a truth table for the given statement. ( ~ p A q ) V ~ q p ~P NPA q Nq ( ~ P A q ) V Nq T T T F T F Need Help? Read ItConstruct a truth table for the given statement. pv (p -> q) p p- q pv (p- q) T T T T F F Need Help? Read It 4. [-/32 Points] DETAILS SMITHNM13 3.2.022. Construct a truth table for the given statement. PA ( q v up ) vr D q v up PA (qv up) PA ( q v up ) vr T T F T F T T T F T5. [-/6 Points] DETAILS SMITHNM13 3.2.027. Write the converse, inverse, and contrapositive of the statements. (a ) ~p - ~q Converse: Op - ~q O ~ q - p do - b~ O O q - p Op - q Inverse: Op - ~q O ~ q - p O ~ q - ~p O q - p Op - q Contrapositive: Op - ~q O ~ q - P O ~ q - up O q - p Op - q\f6. [-13 Points] DETAILS SMITHNM13 3.2.030. Write the converse, inverse, and contrapositive of the statement. If you brush your teeth with Smiles toothpaste, then you will have fewer cavities. Converse: Q If you do not brush your teeth with Smiles toothpaste, then you will not have fewer cavities. Q If you have fewer cavities, then you brush your teeth with Smiles toothpaste. Q If you do not have fewer cavities, then you brush your teeth with Smiles toothpaste. Q If you do not have fewer cavities, then you do not brush your teeth with Smiles toothpaste. Q If you have fewer cavities, then you do not brush your teeth with Smiles toothpaste. Inverse: Q If you have fewer cavities, then you do not brush your teeth with Smiles toothpaste. Q If you have fewer cavities, then you brush your teeth with Smiles toothpaste. Q If you do not brush your teeth with Smiles toothpaste, then you will have fewer cavities. Q If you do not have fewer cavities, then you do not brush your teeth with Smiles toothpaste. Q If you do not brush your teeth with Smiles toothpaste, then you will not have fewer cavities. Contrapositive: 0 If you do not brush your teeth with Smiles toothpaste, then you will not have fewer cavities. Q If you do not have fewer cavities, then you do not brush your teeth with Smiles toothpaste. Q If you do not have fewer cavities, then you brush your teeth with Smiles toothpaste. Q If you have fewer cavities, then you brush your teeth with Smiles toothpaste. Q If you have fewer cavities, then you do not brush your teeth with Smiles toothpaste. Need Help? m 7. [-l1 Points] DETAILS SMITHNM13 3.2.033. Translate the sentence into if-then form. All good people go to heaven. 0 If you do not go to heaven, then you are not a good person. 0 If you are not a good person, then you will go to heaven. 0 If you go to heaven, then you are a good person. 0 If you are a good person, then you will go to heaven. 0 If you are not a good person, then you will not go to heaven. Need Help? _ml 8. [-l1 Points] DETAILS SMITHNM13 3.2.037. Translate the sentence into if-then form. All work is noble. (Thomas Carlyle) 0 If it is not work, then it is not noble. 0 If it is work, then it is noble. Q If it is not noble, then it is not work. Q If it is noble, then it is not work. Q If it is noble, then it is work. Need Help? 9. {-11 Points] DETAILS SMITHNM13 3.2.039. MY NOTES | ASK YOUR TEACHER First decide whether the simple statement is true or false. Then state whether the given compound statement is true or false. If5+10= 18,then1610=4. O F > F is F O F > T is T O F > F is T O T > F is F O T > F is T Need Help? 10. [-I3 Points] DETAILS SMITHNM13 3.2.043. MY NOTES | ASK YOUR TEACHER Tell if the statements are true or false. Let p:4+3=7;q:149=S. (a) \"P V q O True 0 False (b) \"P A "'1? 0 True 0 False (C) \"(P A Q) 0 True 0 False Need Help? 11. [-/3 Points] DETAILS SMITHNM13 3.2.045. MY NOTES ASK YOUR TEACHER PRACTICE Tell if the statements are true or false. Let p: 4 + 5 = 6; q: 4 + 4 = 8. (a) ( p ~ ~q) AP O True O False (b) pv (p - q) O True O False ( c ) ( p q ) - p O True O False Need Help? Read It 12. [-/1 Points] DETAILS SMITHNM13 3.2.048. MY NOTES ASK YOU Translate the statement into symbolic form. (Let a: The amount on line 31 is less than $26,673; c: A child lives with you; p: You turn to page 27.) If the amount on line 31 is less than $26,673 and a child lives with you, turn to page 27. O (a v c) - p Oa - (cvp ) O ( ~a v ~ C ) - up O ( a A ~ C ) - up O ( a A C ) - P Need Help? Read It13. [-/1 Points] DETAILS SMITHNM13 3.2.052. MY NOTES ASK YOUR TEACHER Translate the statement into symbolic form. (Let /: The income on line 1 was reported on Form W-2; s: The "Statutory employee" box on Form W-2 was checked; t: You see instructions for line 1 (Schedule C); c: You check here.) If the income on line 1 was reported to you on Form W-2 and the "Statutory employee" box on that form was checked, see instructions for line 1 (Schedule C) and check here. O ( ~in s ) - (t A C ) O ( iv s ) - (tv c ) O ( in s ) - ( t AC ) O ( ins ) - (tv c ) O ( iv s ) - (t A C ) Need Help? Read It