UNIT-1 Assignment Questions
1.(a) Construct the truth table for S : (P → Q )  (P  Q ) .
(b) Show that the conclusion C : P follows from the premises:
H 1 : P  Q, H 2 : (Q  R ) and H 3 : R.
2.(a) Construct the truth table for (P  (Q  R )) .
(b) Prove that t is a valid conclusion from the premises
p → q, q → r , r → s, s and p  t.
3.(a) Construct the truth table for S : (P  (Q  R) )  ((Q  R)  ( P  R ) ) .
(b) Show that R  (P  Q ) is a valid conclusion from the premises P  Q, Q → R, P → M and M .
4.(a) Construct the truth table for (P  Q )  (R  S ) .
(b) Show that R  S can be derived from the premises P → Q, Q → R, R, P  (R  S ).
5.(a) Show that (Q  ( P  Q) )  (P  Q ) is a tautology.
(b) Show that R  S is a valid conclusion from the premises
C  D, C  D → H , H → ( A  B ) and ( A  B ) → (R  S ).
6.(a) Show that the premises P → Q, P → R, Q → R, P are inconsistent.
(b) Show that p → (q  r )  ( p → q )  ( p → r.)
7.(a) Check the following proposition is a tautology. (( P → Q) → R )  P.
(b) Using the laws of logic show that ( p  q ) → (p  (p  q) )  p  q .
8.(a) Show that the premises R → Q, R  S , S → Q, P → Q, P are inconsistent.
(b) Without using truth tables prove that (p  q )  ( p  ( p  q ) )  p  q.
9.(a) Show that (P  Q ) → (P  Q ) is a tautology.
(b) Show that (p  (q  r ) )  (q  r )  ( p  r )  r
10.(a) Show that (P  (Q  R ) )  (Q  R )  (P  R )  R.
(b) Using the laws of logic show that
( p  q ) → ( p  q ) is a tautology.
11.(a) Obtain DNF & PCNF of P→ [(𝑃 → 𝑄)˄¬(¬𝑄¬𝑃)]
(b) Obtain CNF of¬(𝑃˄𝑄) ↔ 𝑃˄𝑄
12.Show that the following statements are not valid.
Whenever the system software is being upgraded, users cannot access the file system. If users can
access the file system, then they can save new files. If users cannot save new files then the system
software is not being upgraded.
13.Without using truth table find the PCNF and PDNF of P→ (𝑄˄𝑃)˄(¬𝑃 → (¬𝑄˄¬𝑅))
14.Obtain PDNF of
(P˄Q) ˅ (¬𝑃˄𝑅)
( i) Using truth table . (ii) Without using truth table
15. Check the following set of premises is inconsistent.
i.
If Tharun gets degree, he will go for a job.
ii.
If he goes for a job, he will get married soon.
iii.
If he goes for higher study, he will not get married.
Tharun gets his degree and goes for higher study