You just need to learn to use the rules for placing T's and F's
under the columns with ~, ^, v, →, ↔
Rules for putting T or F:
~T becomes F, ~F becomes T
T^T becomes T, anything else with ^ becomes F
FvF becomes F, anything else with v becomes T
T→F becomes F, anything else with → becomes T
T↔T, F↔F both become T, anything else with ↔ becomes F
Now you fill in the missing T's, F's by the rules above
I've filled the T's and F's under the columns for the
single letters p, q, r.
1. ~(p^q)
p | q | p^q | ~(p^q) |
T | T | | |
T | F | | |
F | T | | |
F | F | | |
2. ~pv~q
p | q | ~p | ~q | ~pV~q) |
T | T | | | |
T | F | | | |
F | T | | | |
F | F | | | |
3. (p^q)→(pV~q)
p | q | r | ~q | p^q | pV~q | (P^q)→(pV~q) |
T | T | T | | | | |
T | T | F | | | | |
T | F | T | | | | |
T | F | F | | | | |
F | T | T | | | | |
F | T | F | | | | |
F | F | T | | | | |
F | F | F | | | | |
4. ~q→(p↔r)
p | q | r | ~q | p↔r | ~q→(p↔r) |
T | T | T | | | |
T | T | F | | | |
T | F | T | | | |
T | F | F | | | |
F | T | T | | | |
F | T | F | | | |
F | F | T | | | |
F | F | F | | | |
Edwin
