MA21 EXAM 2 Supplementary Review Write a negation of the statement.

Fall 200

1) Some athletes are musicians.

1)

2) Everyone is asleep.

2)

Let p represent the statement, "Jim plays football", and let q represent "Michael plays basketball". Convert the compound statements into symbols. 3) Jim does not play football or Michael does not play basketball.

3)

Write the compound statement in symbols. Let r = "The food is good," p = "I eat too much," q = "I'll exercise." 4) If the food is good or if I eat too much, I'll exercise.

4)

Determine how many distinct cases must be listed in the truth table for the compound statement. 5) (p O q) O (~r B s) B ~t

5)

6) ~(p O q) B (q B ~r)

6)

Construct a truth table for the statement. 7) (p B ~q) B r

7)

Let p represent a true statement, while q and r represent false statements. Find the truth value of the compound statement. 8) (p B ~q) B r

8)

9) ~[(~p B q) O r]

9)

10) ~[(~p B ~q) O ~q]

10)

11) ~(p B q) B (r O ~q)

11)

12) [(~p B ~q) O ~q]

12)

13) ~[~p B (~q O p)]

13)

Construct a truth table for the statement. 14) ~[p ˙ (~q)]

14)

15) ~(p ¬ q) ¬ (p B ~q)

15)

Given p is true, q is true, and r is false, find the truth value of the statement. 16) (~p B q) ˙ ~r

16)

17) ~q B (p B ~r)

17)

18) (q O r) ˙ (p B q)

18)

1

19) (~p ˙ ~q) B (p ˙ ~r)

19)

Determine the truth value for each simple statement. Then, using the truth values, give the truth value of the compound statement. 20) 9 - 4 = 5 if and only if 11 + 5 = 17.

20)

21) 13 + 1 = 7 if and only if 10 = 14.

21)

State and use DeMorgan's laws or a truth table to determine whether the two statements are equivalent. 22) ~(p O q) ¬ r, (~p B ~q) ¬ r

22)

23) p O q, ~(~p B ~q)

23)

24) p ˙ (q O r), ~p ¬ (q B r)

24)

Write the contrapositive of the statement. Then use the contrapositive to determine whether to conditional statement is true or false. 25) If 10 does not divide the counting number, then 5 does not divide the counting number.

25)

26) If a is not an even counting number, then the product of a and the counting number b is not an even counting number.

26)

Use truth tables to test the validity of the argument. 27) p O q q Tp

27)

28) p ¬ q ~q

28)

T ~p 29)

29) p B ~q pOq Tp Determine if the argument is valid or invalid. Give a reason to justify answer. 30) If you read, then you will have a high score. You do not read. T You will not have a high score.

30)

31) If the bough breaks, then the cradle will fall. The bough breaks. T The cradle will fall.

31)

Use an Euler diagram to determine whether the syllogism is valid or invalid. 32) Some investments are risky. Real estate is an investment. T Real estate is risky.

32)

2

33) Football and studying don't mix. Don is a football player. T Don does not study.

33)

Decide whether the statement is true or false. 34) Every whole number is a real number.

34)

35) Some rational numbers are irrational.

35)

36) Some real numbers are integers.

36)

37) For every real number r, r < 6 or r > 5.

37)

True or false? You MUST justfify your answer! 38) When using a truth table, the statement ~(~q) is equivalent to q.

38)

39) When using a truth table, the statement q ¬ p is equivalent to ~q O p.

39)

40) When using a truth table, the statement ~q B p is equivalent to ~q ¬ p.

40)

41) When using a truth table, the statement q ¬ p is equivalent to ~p ¬ ~q.

41)

42) When using a truth table, the statement ~(q ¬ p) is equivalent to q B ~p.

42)

Write the converse, inverse, or contrapositive of the statement as requested. 43) ~q ¬ ~p

43)

Contrapositive 44) q ¬ ~p Inverse

44)

Find the truth value of the statement. 45) 6 + 1 = 13 if and only if 3 = 9.

45)

46) 9 - 3 = 6 if and only if 8 + 4 = 13.

46)

47) 5 x 2 = 14 if and only if 8 + 9 = 17.

47)

48) Construct the Electric Circuit for (~pOq)¬(qBr)

48)

49) Construct the Electric Circuit for p˙(q B r)

49)

50) Construct the Electric Circuit for

50)

(qO~p)¬~r

3

Answer Key

1) Answer: No athletes are musicians. 2) Answer: Not everyone is asleep. 3) Answer: ~p O ~q 4) Answer: (r O p) ¬ q 5) Answer: 32 6) Answer: 8 7) Answer: p

q

r

T T T T F F F F

T T F F T T F F

T F T F T F T F

(p B ~q) B r F F T F F F F F

8) Answer: FALSE 9) Answer: TRUE 10) Answer: FALSE 11) Answer: TRUE 12) Answer: TRUE 13) Answer: TRUE 14) Answer: p

q

~[p ˙ (~q)]

T T F F

T F T F

T F F T

15) Answer: p

q

T T F F

T F T F

~(p ¬ q) ¬ (p B ~q) T T T T

16) Answer: False 17) Answer: False 18) Answer: True 19) Answer: True 20) Answer: False 21) Answer: True 22) Answer: Equivalent 23) Answer: Equivalent 24) Answer: Not equivalent 25) Answer: If 5 divides the counting number, then 10 divides the counting number. false 26) Answer: If the product of a and the counting number b is an even counting number, then a is an even counting number. false 1

Answer Key

27) Answer: Invalid 28) Answer: Valid 29) Answer: Valid 30) Answer: Invalid by fallacy of the inverse, or show truth table. 31) Answer: Valid by the law of detachment, or show truth table 32) Answer: Invalid 33) Answer: Valid 34) Answer: TRUE 35) Answer: FALSE 36) Answer: TRUE 37) Answer: TRUE 38) Answer: TRUE 39) Answer: TRUE 40) Answer: FALSE 41) Answer: TRUE 42) Answer: TRUE 43) Answer: p ¬ q 44) Answer: ~q ¬ p 45) Answer: TRUE 46) Answer: FALSE 47) Answer: FALSE 48) Answer: Will be provided in class 49) Answer: Will be provided in class 50) Answer: Will be provided in class

2