700 Appendix C • Answers & Hints for Selected Exercises
(c) Since this is true Vx ~a> 0, it is true for all x > 0.
Appendix
EXERCISE SET A.1-A- ,...., (EV P) or,...., E/\,...., P
- Y /\ (E =? A)
3. (H /\ B)/\ ,...., (H /\ B /\ R)
7. ("' S v F) *"' P - P =? [B /\ L/\ ,...., (D VI)] 11. (D4 /\ D3) =? D1 2
(^13) · I ~ I ~ I ~ I ~ I p /\; Q I Q ~ R I R ; s I
- (a) A=? U (b) W =? E (c) (,....,WV,...., U) *"'A
(d) (E =? W)/\,...., (E =? U)
(e) If I understand the basic ideas and I work hard, I enjoy mathematics.
(f) If the assignment is not easy, then I don't understand the basic ideas
or I don't work hard.
(g) It is not true that if I enjoy mathematics then if I work hard the
assignment will be easy.
EXERCISE SET A.1-B- p ,....,p PVrvP 3. p Q PVQ P =? (Pv Q)
T F T T T T T
F T T T F T T
F T T T
F F F T - p ,....,p P/\,...., p rv(P/\rvP)
T F F T
F T F T - p Q R PVQ PVR (P V Q) =? (P V R)
T T T T T T
T T F T T T
T F T T T T
T F F T T T
F T T T T T
F T F T F F
F F T F T T
F F F F F T
(not a tautology)