Solutions
Problem 1 : Exercise Set 2.2, #50, page 50
a. (p->(q->r)) <-> ((p ^ q) -> r)
(p->(~q v r)) <-> (~(p ^ q) v r)
(~p v (~q v r)) <-> (~p v ~q) v r))
~p v (~q v r) <-> ~p v (~q v r)
~p v ~q v r
b. ~(p ^ q ^ ~r)
Problem 2 : Exercise Set 2.3, #11, page 62
| p |
q |
r |
qvr |
~p |
~q |
~r |
~qv~r |
~pv~r |
p->(qvr) |
| T |
T |
T |
T |
F |
F |
F |
F |
F |
T |
| T |
T |
F |
T |
F |
F |
T |
T |
T |
T |
| T |
F |
T |
T |
F |
T |
F |
T |
F |
T |
| T |
F |
F |
F |
F |
T |
T |
T |
T |
F |
| F |
T |
T |
T |
T |
F |
F |
F |
T |
T |
| F |
T |
F |
T |
T |
F |
T |
T |
T |
T |
| F |
F |
T |
T |
T |
T |
F |
T |
T |
T |
| F |
F |
F |
F |
T |
T |
T |
T |
T |
T |
Invalid
Problem 3 : Exercise Set 2.3, #30, page 62
p = This computer program is correct
q = It produces correct o/p.
p -> q
q
Therefore p
Converse Error
Problem 4 : Exercise Set 2.3, #44, page 63
1
c. ~s -> ~t
e. ~s
So ~t--------------Modus ponens
2
g.w v t
1.~t
So w-----------------Elimination
3
d.~qvs
e. ~s
So ~q------------------Elimination
4
a.p->q
3.~q
So ~p----------------Modus Tollens
5
b. rvs
e. ~s
So r----------------Elimination
6
4. ~p
5. r
So ~p^r------------Conjuction
7
~p ^ r -> u
6.~p^r
So u---------------Modus Ponens
8
2. u
7. w
So u ^ w---------Conjuction
Problem 5 : Exercise Set 3.1, #16bdf, page 107
b. For every real no. x , x is positive,negative or zero.
d. For every logician x, x is not lazy.
f. For every no. x, x^2 is not -1.
Problem 6 : Exercise Set 3.2, #15bde, page 116
b. True
d. True
e. False eg: x = 36
Problem 7 : Exercise Set 3.2, #17, page 116
There exists integer d such that 6/d is an integer and d is not equal to 3.
Problem 8 : Exercise Set 3.3, #28, page 130
a. True - d and e, f and h
b. For every triangle x and for every square y, x is not above y or x and y have different color.
Problem 9 : Exercise Set 3.4, #27, page 143
Nothing intelligible ever puzzles me.
It means if something is intelligible then it does not puzzle me.
But logic puzzles me.So logic is not intelligible.
Set U : Intelligible
Set I : Not puzzling where I is a subset of U
and set L : Logic independent set outside of U.