07–
Conditional Propositions and Truth Tables
Note:
The tilde (~) may be used to denote a logical inversion, or NOT, operation.
The
symbol v is used to represent the OR operator, while the ^
symbol represents the AND operator.
For
problems 1-5, evaluate each proposition for the truth values where p is false, q is true, and r is
false.
1. p →
q
2. Øp → Øq
3. Ø (p
→ q)
4. (p → q) ^ (q → r)
5. (p → q) → r
For
problems 6-10 use truth tables to determine if each pair of propositions is
equivalent. Identify whether they are, in fact, equivalent.
6. p
p ^ Øq
e.g. is p equivalent to p ^ Øq for every combination of truth values of p
and q?
7. p ^ q
Øp v Øq
8. p → q
Øp v q
9. p → q
Øq → Øp
10. (p →
q) ^ (q → r)
p → r
Formulate
the symbolic expression in words
using the following text:
p: Today is Tuesday
q: it is raining
r: it is cold
11. p → q
12. Øq → (r ^ p)