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Que. Consider a weighted undirected graph with positive edge weights and let uv be an edge in the graph. It is known that the shortest path from the source vertex s to u has weight 53 and the shortest path from s to v has weight 65. Which one of the following statements is always true?
a. weight (u, v) < 12
b. weight (u, v) ≤ 12
c. weight (u, v) > 12
d. weight (u, v) ≥ 12
Answer:weight (u, v) ≥ 12
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Similar Questions:

An ordered n-tuple (d1, d2, … , dn) with d1 >= d2 >= ⋯ >= dn is called graphic if there exists a simple undirected graph with n vertices having degrees d1, d2, … , dn respectively. Which of the following 6-tuples is NOT graphic?
The decimal value 0.25
Let R1 be a relation from A = {1, 3, 5, 7} to B = {2, 4, 6, 8} and R2 be another relation from B to C = {1, 2, 3, 4} as defined below:

1. An element x in A is related to an element y in B (under R1) if x + y is divisible by 3.
2. An element x in B is related to an element y in C (under R2) if x + y is even but not divisible by 3.

Which is the composite relation R1R2 from A to C?  
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P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even.
Consider the following statements:

S1: There exists infinite sets A, B, C such that
A ∩ (B ∪ C) is finite.
S2: There exists two irrational numbers x and y such
that (x+y) is rational.

Which of the following is true about S1 and S2?
For the set N of natural numbers and a binary operation f : N x N → N, an element z ∊ N is called an identity for f, if f (a, z) = a = f(z, a), for all a ∊ N. Which of the following binary operations have an identity?

1. f (x, y) = x + y - 3
2. f (x, y) = max(x, y)
3. f (x, y) = x^y
How many undirected graphs (not necessarily connected) can be constructed out of a given set V = {v1, v2, ... vn} of n vertices?
Consider the binary relation R = {(x, y), (x, z), (z, x), (z, y)} on the set {x, y, z}. Which one of the following is TRUE?
Which of the following is true?
If X, then Y unless Z" is represented by which of the following formulae in propositional logic? ("¬" is negation "^" is conjunction, and "→" is implication)
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