If p is false and q is true, determine the truth value of the following:
a) ~(p ^ q) = ~(F ^ T) = ~(F) = T
b) p v ~q = F v ~T = F v F = F
c) ~(p → q) = ~(F → T) = ~(F) = T
d) ~p → q = ~F → T = T → T = T
e) p ↔ ~q = F ↔ ~T = F ↔ F = T
~ is T when followed by F and vice-versa.
^ is T only when it has a T on each side of it, otherwise it's F
v is T unless it has 2 F's on each side of it.
→ is T unless it is a case of T→F
Use truth tables to determine if p → q is identical (equivalent)
to ~p v q
p q ~p ~p v q | p → q
-----------------|-------
T T F T | T
T F F F | F
F T T T | T
F F T T | T
They are equivalent because both their truth tables go TFTT.
Edwin
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