Here you can compute the truth values of 16 statements about the crew of a ship,
consisting of four persons: captain, engineer, sailor, and cook.
You should fill out the following 4*4 table with the ages, heights, education, and gender
of your crew. By clicking on the "Check" button you can evaluate the truth values.
You may also write "T" or "F" in the fields at the beginning of some statements. Then the long text field shows you where the truth values of the statements considered differs from your choice. You may also click the button "satisfy conditions"---in that case the computer tries whether one of 100 random crews satisfies all required conditions.
some member of the crew is female
6) each crew member is at least twice as high as old.
7) no female is larger than 190 (cm).
8) each crew member is larger than 192 (cm)
|9) none of the crew members has finished high school.|
|10) at least one crew member is not older than 30, or female, (or both)|
a) Write the negations of all these statements above in plain English.
c) Check whether the conjunction of statements # 5, 7, and 8 is satisfiable. That is, find out whether it is possible to create a crew where all the statements # 5, 7, 8 are true. If it is possible, show the crew. If it is impossible, show why not.
d) Check whether the conjunction of statements 4, 10, 11, and the negation of statement #1 is satisfiable.
e) Assume that statements # 4, 10, and 11 are true. Which of the statements above (or their negations) must follow then? Why?
f) Assume that statements # 5, 9, 11, and 12 are true. Which of the statements above (or their negations) must follow then? Why?
f) Express statement # 13 as a compound statement, using only the five prime statements A1:="The captain is female", A2:="The engineer is female", A3:="the sailor is female", A4:="the cook is female", and A5:="the captain has a college degree", and their negations.
Go to Project # 2.