Truth-Tables Flashcards
Considering disjunctions, conjunctions, and conditionals, which says ‘atleast one’ ?
Disjunctions.
Considering disjunctions, conjunctions, and conditionals, which says ‘both’ ?
Conjunctions.
What lines are disjunctions false on?
A disjunction is only false on the last line, where p and q are both false.
What lines are conjunctions false on?
A conjunction is false on every line except the first, where both p and q are true.
What lines are conditionals false on?
A conditional is true on every line except the second, where p is true and q is false.
Given p and q, what are the truth values for the conditional?
T,F,T,T
Given p and q, what are the truth values for a disjunction?
T,T,T,F
Given p and q, what are the truth values for a conjunction?
T,F,F,F
If p is false and q is false, what is the truth value of the conditional?
True. A conditional is true on every line except the second, where p is true and q is false.
If p is false and q is true, what is the truth value of the conditional? Explain.
The restriction on a conditional is that p is true every time q is true. This means, vacuously, that anytime p is false, the conditional is still true.
When is a conjunction true? Explain.
First line. When both p and q are true. This is because the conditions on a conjunction is that it is true only when both conjuncts are true. So, it can’t be true on the other lines, because in those, either p or q is false, and that violates the conditions on a conjunction.
When is a disjunction true?
All lines except the last, where both p and q are false. This is because the conditions on a disjunction is that it is true only when one, or both, of its disjuncts are true. So, it can’t be true on the last line, because there, p and q are false, which would make both disjuncts false, which violates the conditions on a disjunction.
