01 May Q1. Check whether the following statement forms are tautologies or not without using truth
Q1. Check whether the following statement forms are tautologies or not without using truth
table technique.
a. [(p ? q) ? (p ? r)] ? [p ? (q ? r)]
b. (s ? p? ~ r) ? (p ? (r ? q) ? s) ? p ? s
Q2. Are these system specifications consistent? ”The router can send packets to the edge system
only if it supports the new address space. For the router to support the new address space it is
necessary that the latest software release be installed. The router can send packets to the edge
system if the latest software release is installed. The router does not support the new address
space.”
Q3. Prove or disprove the following statements. Clearly indicate what kind of proof technique
you are attempting. For example, you can start like ”We use proof by contradiction”, or ”We
use case analysis” etc. Remember that a good proof is more like an essay and not a sequence of
formulas without explanations, and you should always complete your proof explaining why the
original claim follows.
a. If s is irrational, then v
s is also irrational.
b. ? r, s ? R, max{r, s} + min{r, s} = r + s
c. ? a, n ? Z, if a | n
2 and a = n, then a | n.
d. v
6 + v
5 is irrational.
Q4. Prove that if n is an odd integer, then
a. j
n
2
4
k
=
n-1
2
n+1
2
b. l
n
2
4
m
=
n
2+3
4
.
c. n
3 + n is even.
The remaining questions are for COMP8781 students on
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