construct a truth table for the following statement:
~q(arrow facing right)p
The rule for the conditional p -> q is summarized in the table
p q p -> q
T T T
T F F
F T T
F F T
which shows that p -> q is false only when p is true and q is false.
To set up a table for ~q -> p we need to first set up columns for p and q, which we always require, and also for ~q.
p q ~q
T T F
T F T
F T F
F F T
The column for ~q is the opposite of the column for q, false when q is true and true when q is false.
Then to evaluate ~q -> p we use the rule for the conditional, where the conditional is false only when the expression in front of the -> is true and the expression after the -> is false. In the case of ~q -> p this occurs in only the fourth row, making the fourth-row value of ~q -> p false. The other values of this expression are true.
p q ~q ~q -> p
T T F T
T F T T
F T F T
F F T F
would you do an example of a negation
The above example includes the negation of q. Hopfeully that answers your question. If you need further examples, send me specific questions, and be sure to tell me what you do and do not understand about each.
i'm having trouble with biconditionals in sec 3.4 would you please go over some examples
The biconditional p <-> q means (p -> q) ^ ( q -> p ).
The truth table for the biconditional (p -> q) ^ ( q -> p ) is as follows:
p q p -> q q -> p (p -> q) ^ ( q -> p)
T T T T T
T F F T F
F T T F F
F F T T T
From this we see that the biconditional is true if both p and q have the same truth value (either T T or F F, as in the first and fourth rows of the table) and false if p and q have opposite truth values (either T F or F T as in the second and third rows of the table).
If you need further examples, send me specific questions, and be sure to tell me what you do and do not understand about each.