Chapter 6 Logic

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  • Topic: Logic, Logical connective, Necessary and sufficient condition
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Chapter 6 Exam

Select the correct answer for each question. All questions are worth 4 points a piece.

1. Coors is smooth or both Beck’s is subtle and Guinness is heavy.
a.C (B • G)
b.C • (B G)
c.(C B) • G
d.(C • B) G
e.C B • G

2.Budweiser is bland if either Heineken is balanced or Foster’s is refreshing.
a.(H B) F
b.(B H) F
c.B (H F)
d.B H F
e.(H F) B

3Alaskan is sweet only if neither Heineken is balanced nor Pabst is clean tasting.
a.A (H P)
b.A H • P
c.(H P) A
d.A (H P)
e.(H P) A

4.Sierra is hearty given that Michelob’s being flavorful implies that Guinness is heavy.
a.(S M) G
b.(G M) S
c.S (M G)
d.M (G S)
e.(M G) S

5.Harp is soothing if and only if both Miller is not zesty and Coors is not smooth.
a.H (M • C)
b.(H M) • (H C)
c.H (M • C)
d.(H M) • (H C)
e.H (M • C)

6.Sierra is hearty only if Budweiser is bland, given that both Heineken is balanced and Michelob is complex.
a.(S B) (H • M)
b.(H • M) (S B)
c.(H • M) (B S)
d.(S B) (H M)
e.(H M) • (S B)

7.Corona is drinkable if Pabst is clean tasting, and Foster’s is refreshing only if Guinness is dark.
a.(P C) • (F G)
b.(C P) • (F G)
c.(C P) • (G F)
d.(P F) • (C G)
e.(P C) (F G)

8.Michelob’s being complex is a necessary condition for Heineken’s being balanced unless Alaskan’s being sweet is a sufficient condition for Carlsberg’s being malty.
a.(M H) (A C)
b.(M H) (A C)
c.(M H) (C A)
d.(H M) (A C)
e.(H M) (A C)

9.If Heineken’s being balanced implies that either Sierra is hearty or Alaskan is not sweet, then Miller’s being zesty is a sufficient and necessary condition for Coors’s being smooth.
a.[H (S A)] (M C)
b.[H (S A)] (M C)
c.[H (S A)] (M C)
d.H [(S A) (M C)]
e.H [(S A) (M C)]

Given that A and B are true and X and Y are false, determine the truth values of the propositions in Problems 10 and 12.

10.{[(B X) Y] [ X (A Y)]}
a.True.
b.False.

11.In Problem 10, the main operator is a:
a.Dot.
b.Horseshoe.
c.Wedge.
d.Triple bar.
e.Tilde.
12.[(A Y) • (B X)] • [(B X) • (X A)]
a.True.
b.False.

13.In Problem 12, the main operator is a:
a.Triple bar.
b.Wedge.
c.Tilde.
d.Dot.
e.Horseshoe.

Use ordinary truth tables to answer Problems 14-21. Construct the truth tables as per the instructions in the textbook.

14.Given the statement:(H K) (K H)
This statement is:
a.Self-contradictory.
b.Contingent.
c.Consistent.
d.Logically equivalent.
e.Tautologous.

15.The truth table in Problem 14 has how many lines?
a.Six.
b.Eight.
c.Four.
d.Two.
e.Nine.

16.Given the statement:[G (R • N)] [R (G • N)]
This statement is:
a.Tautologous.
b.Contingent.
c.Inconsistent.
d.Self-contradictory.
e.Consistent.

17.The truth table in Problem 16 has how many lines?...
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