Math 10 Name Exam 2: Chapter 3 Points are as stated. Y o u must s h o w al l w o r k to receive ful l credit.

State whether each statement is true or false. Pomts are al l or nothing ' for true false. 2 points each.

1. " A l l cats are cool" is the negation of "Some cats are cool."

2. "Some is not good" is the negation of "it's all good."

3. An exclusive OR means one, or the other, or both.

4. "Peter Piper picked a peck of pickled peppers" is a complex statement.

5. A quantifier is the same as a connective.

6. Ifp: drink, q: drive, then "don't drink, and drive" is symbolized ~ (pAq).

7. "The best part of waking up is Folder's in my cup" is a conditional statement.

8. Tautologies are statements that are always false.

9. Self contradictions are statements that are always false.

10. A conjunction is only true if both statements are true.

11. DeMorgan's laws are used to write a disjunction as a conditional statement.

12. A l l of the variations of conditional statements have the same truth table outcomes.

13. "If red, then blue" is the converse statement of "If blue, then red."

14. If p ^ q isthe conditional statement, then ~ p ->~ q is the converse statement.

15. If /) -> 9 is the conditional statement, then ~ q ->~ p is the contrapositive statement.

16. If /7 -> ^ is the conditional statement, then q -> p is the inverse statement.

p - ^ q

17. The symbolic argument qAr can be written [(p-> (7) v ((7 A r)] ^ (/? A r).

:. pAr

18. An electrical current can take more than one path in a series circuit.

19. For switching circuits, a false statement means an open switch.

20. For switching circuits, the light comes on when the switch is open.

21. Write the negation of each statement using the proper quantifiers. 2 points each,

a. Everyone is cool. 5c(Y)S c]tfT VAP^ CQC^\

b. No one IS cool. t)CW. cS' * - CCC'\

c. Some are cool.

d. Some aren 7 cool. aft

2 2 . Write the compound statement in symbolic form. 4 points

If you are happy and you know it, then clap your hands.

1: u at V^v:. '(V

symbolic form:

23. Without using a truth table, determine the truth value of the given compound statement. 4 points.

I'm going in, and if I'm not hack in five minutes, then Just wait longer, or I'm not going in.

p: I'm going in (T) q: I'm hack in five minutes (T) r: wait longer fF)

-\ T M V

m

24. Construct a true table for the following statement. 5 points.

Jump around and Jump up, or Jump up and gel: down.

r:

P

T

T T T F F F F

9

T

T F F T T F F

r

T

F

T

F

T

F

T

F

T

25. Write an equivalent statement using the fact that (p -> ^) <=> (~ /»v ^ ) , or the fact that ~ {p ^ q) (pA ~ q) . 4 points.

It is false that if my bologna has a first name, then my bologna doesn't have a second name.

p: my bologna has a first name ' q: my bologna has a second name

26. Write an equivalent statement using De Morgan's Laws. 4 pomts.

No shoes or no service.

nent usmg De Morgan s Laws. 4 points.

p: shoes -r-v "^P^ t ^ ' « i > 3 0 * . W:V\(J<^. q: service ^ ^ C A J C ^

27. Write the converse, inverse and contrapositive of the following statement, v points.

If I can, then I will,

p: I CC)I\

a. Converse:

b. Inverse:

c. Contrapositive:

28. Determine whether the two statements, pv~{qA r) and ~ p

tables. 6 points.

{qAr) are equivalent using truth

P

T T

T

T

F

F

F

F

T T

F

F

T

T

F

F

r T F

T

F

T p

T

F

p v ~ ( ^ A r )

T T F F F F

T r

TiTir TtF

T T F

29. Write an argument in symbolic form. Then use a truth table to determine whether the argument is valid or invalid. 5 points.

P > q P If Who is on first, then What is on second If What is not on second, then Who not is on first: Who is on first. Therefore, Who is on first and What is on second.

p Q

T T F F

T F T F

1 F T m T| F\T\trnT\

|T T F\rlT\

6 0 Mc%^(X 30. Determine whether an argument is valid or invalid by comparing its symbolic form with one of the

standard symbolic forms. State the name of the standard form you are using in the comparison. 4 pomts.

Fallacy of the Converse Fallacy of the Inverse Law of Detachment Law of Contraposition Law of Syllogism

Q ~ P p ~q q ^

Disjunctive Syllogism pvq

~ P

•• P • q

If Jimmy cracks corn, then I don 7 care. I care. Therefore, Jimmy didn 7 cracked corn.

L ^0

D

31. Convert the electrical circuit to a symbolic statement. 4 points.

32. Determine whether the two circuits are equivalent.

P T T i T I T ! F ] F I F

I

F \

T T F F T T F F

r T

F

T

F

T

F

T

F

^ ^ ^ ^ ^ ' ^ p ^ C ^ r ^ T \ T ! I r ^