Question 1 |
Consider the statement
"Not all that glitters is gold"
Predicate glitters(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?
"Not all that glitters is gold"
Predicate glitters(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?
\forall x:glitters(x)\Rightarrow \neg gold(x) | |
\forall x:gold(x)\Rightarrow glitters(x) | |
\exists x:gold(x)\wedge \neg glitters(x) | |
\exists x:glitters(x)\wedge \neg gold(x) |
Question 1 Explanation:
Question 2 |
Suppose you break a stick of unit length at a point chosen uniformly at random. Then the expected length of the shorter stick is
0.25 | |
0.5 | |
0.75 | |
1 |
Question 2 Explanation:
Question 3 |
Let G=(V,E) be a directed graph where V is the set of vertices and E the set of edges. Then which one of the following graphs has the same strongly connected components as G ?
G_{1}=(V,E_{1}) where E_{1}\equiv \{(u,v)|(u,v)\notin E\} | |
G_{2}=(V,E_{2}) where E_{2}\equiv \{(u,v)|(v,u)\in E\} | |
G_{3}=(V,E_{3}) where E_{3}\equiv \{(u,v)| there is a path of lenth \leq 2 from u to v in E} | |
G_{4}=(V_{4},E) where V_{4} is the set of vertices in G which are not isolated |
Question 3 Explanation:
Question 4 |
Consider the following system of equations:
3x + 2y = 1
4x + 7z = 1
x + y + z = 3
x - 2y + 7z = 0
The number of solutions for this system is
3x + 2y = 1
4x + 7z = 1
x + y + z = 3
x - 2y + 7z = 0
The number of solutions for this system is
0 | |
1 | |
2 | |
3 |
Question 4 Explanation:
Question 5 |
The value of the dot product of the eigenvectors corresponding to any pair of different eigenvalues of a 4-by-4 symmetric positive definite matrix is
0 | |
1 | |
2 | |
3 |
Question 5 Explanation:
There are 5 questions to complete.