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CSE - Questions and solutions set-14

Computer science and engineering(CSE) - Question & solution set-14
Question:-
Option (A)
Poset which is not a lattice
Option (B)
A lattice which is not complemented
Option (C)
Complemented lattice
Option (D)
A Boolean algebra
Correct Option:
C
Question Solution:
Since every pair has a lub and glb, it is a lattice. Further more, since every element has atleast one complement as shown below,
a' = g
b' = c, d, f
c' = b, e
d' = b, e
e' = c, d, f
f' = b, e
g' = a
therefore, the lattice is complemented.
Since some elements have more than one complement, the given lattice is not distributive, and hence is not a Boolean algebra.
Question:-
Option (A)
n mod 3 = 0
Option (B)
n mod 5 = 0
Option (C)
n mod 2 = 0
Option (D)
n mod 2 = 1
Correct Option:
C
Question Solution:
If n mod 2 = 0 then n is even and hence the graph has no odd cycle and hence is bipartite.
Question:-
Option (A)
Only (i) and (ii)
Option (B)
Only (ii) and (iii)
Option (C)
Only (i) and (iii)
Option (D)
All (i), (ii) and (iii)
Correct Option:
D
Question Solution:
Put ^ -> . and ∨ -> +
(i)[p ^ (p->q)]->q
=
= pq->q =
=
=
So (i) is tautology.
(ii) (ii) is tautology in the same way as (i)
(iii)
=
=
=
=
=
So (iii) is also topology.
Hence option (d) is true.
Note:
This problem can be done more easily if the following is observed.
(i) is modus ponens and hence is tautology.
(ii) since p -> q , therefore is a tautology.
(iii) is modus tollens and hence is tautology.
Question:-
Option (A)
0.50000
Option (B)
0.45063
Option (C)
0.45018
Option (D)
0.46000
Correct Option:
C
Question Solution:
The equation is f(x) = cos x - 2x
This is equivalent to solving f(x) = 0,
wheref(x)=cos x - 2x
So the recursion formula becomes
xn + 1=
With an initial guess x0 = 0.5
we obtain
x0=0.5
x1=0.45063
x2=0.45018
x3=0.45018
With no further changes in the digits, to five decimal places. Therefore, to this degree of accuracy the root is x = 0.45018
Hence correct answer is (c).