course Mth 151
6/26 10
Question: `q001. There are 8 questions in this set.
If each of the propositions p and q can be either true or false, what combinations of truth values are possible for the two propositions (e.g., one possibility is that p is false and q is true; list the other possibilities)?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
P is true and q is true, p is false and q is false, p is true and q is false, p is false and q is true so its TT FF TF FT
3
Ok
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Question: `q002. For each of the for possibilities TT, TF, FT and FF, what is the truth value of the compound statement p ^ q ?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: .
TT, p is true and q is true so p ^ q is true.TF, p is true and q is false so p ^ q is false. FT, p is false and q is true so p ^ q is false. FF, p is false and q is false so p ^ q is false.
3
Ok
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Question: `q003. Write the results of the preceding problem in the form of a truth table.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
P Q P^Q
T T T
T F F
F T F
F F F
3
Ok
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Question: `q004. For each of the possible combinations TT, TF, FT, FF, what is the truth value of the proposition p ^ ~q?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
TT we have true, q true so ~q is false and p ^ ~q is false. TF we have p true, q false so ~q is true and p ^ ~q is true. FT we have p false, q true so ~q is false and p ^ ~q is false FF we have p false, q false so ~q is true and p ^ ~q is false.
3
Ok
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Question: `q005. Give the results of the preceding question in the form of a truth table.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
p q ~q p^~q
T T F F
T F T T
F T F F
F F T F
3
Ok
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Question: `q006. Give the truth table for the proposition p U q, where U stands for disjunction.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
p q p U q
T T T
T F T
F T T
F F F this is so because it read p or q
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Question: `q007. Reason out the truth values of the proposition ~(pU~q).
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
TT p is true and q is true, so ~q is false. Thus p U ~q is true, since p is true. So ~(p U ~q) is false.TF p is true and q is false, so ~q is true. Thus p U ~q is true, since p is true (as is q). So ~(p U ~q) is false.FT p is false and q is true, so ~q is false. Thus p U ~q is false, since neither p nor ~q is true. So ~(p U ~q) is true.FF p is false and q is false, so ~q is true. Thus p U ~q is true, since ~q is true. So ~(p U ~q) is false.
2
ok
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Question: `q008. Construct a truth table for the proposition of the preceding question.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
p q ~q pU~q ~(pU~q)
T T F T F
T F T T F
F T F F T
F F T T F
3
ok
"
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