L6-DM-UNIT 1-Set Theory, Mathematical Induction, CNF, DNF- PROBLEM SOLVING | SPPU | SE Comp

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UNIT 1- SUMMARY
NUMERICAL PROBLEM SOLVING

S.E. (Computer) (I Sem.) DEC- 2017
1. (a) [6-MARKS]

Define following with proper set notations and examples:
Membership
Proper subset
Power sets
Empty sets
Cardinality of sets
Multisets

S.E. (Computer) (I Sem.) DEC- 2019
2. (b) [3-MARKS]

Let A={𝜙,𝑏} construct the following set
A- 𝜙
{𝜙}-A
AUP(A) where P(A) is power set.

S.E. (Computer) (I Sem.) MAY-2019
Q 2. (a) [3-MARKS]

What is a multiset.
Let P and Q are two multiset defined as
P={a,a,a,c,d,d}
Q={a,a,b,c,c}
Obtain union, intersection, difference of two multiset P and Q.

S.E. (Computer) (I Sem.) DEC- 2019
1. (a) [3-MARKS]

Prove that set of rational numbers is countably infinite.
(MAY-2019 Q 2. (B) [3-MARKS] )

S.E. (Computer) (I Sem.) DEC-2019
2. (a) [3-MARKS]

In a survey of 60 people :
25 read newsweek magazine (N)
26 read time (T)
26 read fortune (F)
9 read both newsweek and fortune (N ∩ F)
11 read both newsweek and time (N∩ T)
8 read both time and fortune (T ∩ F)
8 read no magazine at all. (TOTAL -NUFUT)

(i) Find the no. of people who read all the three magazines.
(ii) Find the no. of people who read exactly one magzine.

S.E. (Computer) (I Sem.) DEC-2018
1. (b) [2-MARKS]
Use :
p : I will study discrete structure
q : I will go to a movie
r : I am in a good mood.
Write the English sentence that corresponds to each of the following :
(i) ~ r q
(ii) ~ q ^ p
(iii) q  ~ p
(iv) ~ p  ~ r.

S.E. (Computer) (I Sem.) DEC-2019
(b) [3-MARKS]

Show that for all natural numbers n:
1^3+2^3+3^3+⋯+𝑛^3=(1+2+3+⋯+𝑛)^2

S.E. (Computer) (I Sem.) DEC-2019
2. (a) [3-MARKS]
Find DNF (Disjunctive normal form ) of:
Find CNF (Conjunctive normal form ) of: