Formal Logic

Question 1

“If A, then B” State the contrapositive.

Answer 1

If -B, then -A

Question 2

If it is a cloudless day, the sky is a clear blue.” State the contrapositive.

Answer 2

If the sky is not a clear blue, then it is not a cloudless day.

Question 3

“If A, then (B1 or B2) and C.” State the contrapositive.

Answer 3

If not B1 AND B2 OR not C, then not A

Question 4

“If the flag is up on the hill, then we know George or Montbleu must be at work.” State the contrapositive.

Answer 4

If NEITHER George NOR Montbleu are at work, then the flag is not up on the hill.

Question 5

“Whenever the elephant raises its trunk or lets out a bellow, then it is both angry and alone.” State the contrapositive.

Answer 5

If the elephant is not angry OR not alone, then it NEITHER raises its trunk NOR lets out a bellow.

Question 6

“A only if B”

restate as an if/then statement.

Answer 6

If B then A.

Question 7

“Z only if X”

State the contrapositive

Answer 7

If not Z, then not X.

Question 8

“Edelin is kind only if she has plenty to eat or she has had plenty of sleep.”

State the contrapositive.

Answer 8

If Edelin is not kind, then she has not had plenty to eat AND she has not had plenty of sleep.

Question 9

“If A, then B or C”

State the minimum information needed to negate A.

Answer 9

-B AND -C

Question 10

“If A, then B and C”

State the minimum information needed to negate A.

Answer 10

-B OR -C

Question 11

“A and B are not both selected together.”

List all logical deductions.

Answer 11

If A then Not B

If B then Not A

Question 12

“If A is selected B is also selected.”

List all logical deductions

Answer 12

If A then B

If Not B then Not A

Question 13

“If A is not selected B is selected.”

List all logical deductions.

Answer 13

If Not A then B

If Not B then A

= Either A or B or Both Must be selected.

Question 14

“A is selected whenever B is not selected.” List all logical deductions

Answer 14

If Not B then A

If Not A then B

= Either A or B or Both Must be selected.

Question 15

“Neither A or B is selected if C is selected.” List all logical deductions.

Answer 15

If C then Not A AND Not B

If A OR B then Not C

Question 16

“If A is selected, both B and C must be selected.” List all logical deductions.

Answer 16

If A then B AND C

If Not B OR Not C then Not A

Question 17

“Only if A is selected will B be selected.”

List all logical deductions

Answer 17

If B then A

If Not A then Not B

Question 18

“The printer functions adequately only if the sun is at the correct angle and leprechauns are dancing.” List all logical deductions

Answer 18

If the printer is not functioning adequately, then the sun is not at the correct angle OR leprechauns are not dancing.

If the sun is at the correct angle, and leprechauns are dancing, then the printer functions adequately.

Question 19

“Kant is a trustworthy ethicist only if John Stuart Mill is not trustworthy.” State all logical deductions.

Answer 19

If JSM is not trustworthy, then Kant is a trustworthy ethicist.

If JSM is trustworthy, then Kant is not a trustworthy ethicist.

Either JSM is trustworthy or Kant is trustworthy.

Question 20

“Aristotle and Plato can’t both be right.” State all logical deductions.

Answer 20

If Aristotle is right, then Plato is not right.

If Plato is right, then Aristotle is not right.

Question 21

“Marx is correct only if Hegel and Adam Smith were asleep on the job.” State all logical deductions.

Answer 21

If BOTH Hegel and AS were asleep on the job, then Marx was correct.

If Marx was not correct, then either Hegel OR Adam Smith were not asleep at the job.

Question 22

“If Aquinas got the facts straight, then Anselm and Augustine were also correct.” State the contrapositive.

Answer 22

If EITHER Anselm OR Augustine were not correct, then Aquinas did not get the facts straight.