Practice In Symbolizing
: Using each of the sentence letters listed below, symbolize each of the following statements. Answers follow the list of problems.
P = penguins are perky
Q = quail are quiet
R = rats are ratty
S = snails are snappy dressers
T = Elizabeth Taylor eats a horse
1. When penguins are perky quail are quiet.
2. If quail are quiet and rats are ratty, Elizabeth Taylor will eat a horse.
3. Either snails are snappy dressers or penguins are perky.
4. Rats are ratty just in case quail are quiet.
5. All times quail are quiet are times rats are ratty.
6. If it's not the case that snails are snappy dressers, then either quail are quiet or Elizabeth Taylor eats a horse.
7. If rats aren't ratty, then quail aren't quiet.
8. Neither rats are ratty nor are quail quiet.
9. Only when quail are quiet does Elizabeth Taylor eat a horse.
10. Quail are quiet only when Elizabeth Taylor eats a horse. 11. When either quail are quiet or penguins are perky, rats are ratty and Elizabeth Taylor eats a horse.
12. It's untrue that penguins are perky provided that quail are quiet.
13. It's untrue that it is not that case that neither rats aren't ratty nor penguins are un- perky.
14. If either snails are snappy dressers or penguins are perky, then if Elizabeth Taylor eats a horse, penguins are perky.
15. If rats are ratty, and if quail are quiet, then if penguins are perky, then rats are ratty if and only if quail are quiet.
16. If quail are quiet when rats are ratty, and rats are ratty whenever quail are quiet, then quail are quiet if and only if rats are ratty or, rats are ratty if and only if quail are quiet.
1. P -> Q
2. (Q & R) -> T
3. S v P
4. R <-> Q
5. Q -> R
6. ~S -> (Q v T)
7. ~R -> ~Q
8. ~R & ~Q
9. T -> Q
10. Q -> T
11. (Q v P) -> (R & T)
12. ~(Q -> P)
13. ~~(~R & ~P)
14. (S v P) -> (T -> P)
15. (R & Q) -> (P -> (R <-> Q))
16. ((R -> Q) & (Q -> R)) -> ((Q <-> R) v (R <-> Q)).