Solutions (or Hints) to
Chapter-end Exercises
Chapter 1
1.1 All the sentences except (g) are propositions.
1.2 Let L, E, and G denote a < b, a = b and a > b respectively. Then
the sentence can be written as
(E 1\ , G 1\ , L) v (G 1\ , E 1\ , L) v (L 1\ , E 1\ , G).
1.3 (i) David gets a first class or he does not get a first class. Using the
truth table given in Table A1.I, v is associative since the columns
corresponding to (P v Q) v Rand P v EQ v R) coincide.
TABLE A1.1 Truth Table for Exercise 1.3
P
Q
R
P v Q
Q v R (P v Q) v R P v (Q v R)
T
T
T
F
F
T
T
T
T
F
F
T
F
F
T
F
T
T
T
F
F
T
F
F
T
F
T
T
F
T
T
T
F
F
F
F
T
F
T
T
T
T
F
F
T
F
T
T
T
F
F
F
F
T
F
F
The commutative and distributive properties of Exclusive OR can be
proved similarly.
1.4 Using v and " all other connectives can be described. P 1\ Q and
P :::::> Q can be expressed as , (, P v , Q) and, P v Q respectively.
1.5 ,P = p i p
P 1\ Q = (P i Q) i (P i Q)
P v Q = (P i P) i (Q i Q)
Verify these three equations using the truth tables.
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