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Important Questions.
PART. A
1.Define tautology with an example
2. Find the dual of Pv (QAR)v F
3. Give the converse and the contrapositive of the implication “if it is raining, then
get wet”
4. State the principle of mathematical induction.
5. State the pigeonhole principle
6. Detine proposition
7Define tautology with an example
8.Write the symbolic representation of “if it rains today, then I buy an umbrella”
9. State the pigeonhole principle
10. How many permutations are there in the word MISSISSIPPI?
PART- B
1. Prove that (P > Q)A(Q > R)=> (P > R)
2. Obtain PDNF and PCNF for (PAR)v (PA=Q).
3. Show that (x)(P(x) > O(e)) > (x)P(e) > (xJO(x)
4. Prove that the premises P > 0,0 > R,R—> S,S > aR and PAS are
inconsistent.
5.. Show that (xP(x) > Q(x)) = (x)P(x) > (x)O(x).
6. Use mathematical induction, prove that
lee 1
t+ ttt yn forn > 2
vi v2 V3 V4 vn
7.What is the maximum number of students required in a discrete mathematics class
to be sure that atleast six will receive the same grade if there are five possible
Grades A ,B,C,D and E?
8. State the strong induction (the second principle of mathematical induction). Prove
that a positive integer >1 is either a prime number or it can be written as product
of prime numbers.
9. A bag contains six white balls and five red balls. Find the number of ways four
balls can be drawn from the box if
(1). They can be any colour.
(2). Two must be white and two red.
(3). They must all be the same colour.
10. Obtain the principle disjunctive form of (=P > R)A(Q < P)
(i).Using truth table (ii) without using truth table
11. Obtain PDNF and PCNF for (PAQ)v (—PAR).
12. Show the following premises are inconsistent
(i). If Ravi misses many classes through illness that he fails high school
(ii). If Ravi fails high school, then he is uneducated
(iii). If Ravi reads a lot of books, then he is not uneducated
(iv). Ravi misses many classes through illness and reads a lot of books. 13, Show that RA(P v Q)is a valid conclusion from the premises
(PvQ),07R,P>M,-M.
14.State and prove the generalised pigeonhole principle.
+ ALL THE BEST#H#HH#t
2021.9.27 10:34
