Directions: A, B, C, D, E, F, and G are travelling in three different vehicles. There are at least two passengers in each vehicle: Swift, Creta, Nexon, and only one of them is a male. There are two engineers, two doctors, and three teachers among them.
(i) C is a lady doctor and she does not travel with the pair of sisters A and F.
(ii) B, a male engineer, travels with only G, a teacher, in a Swift.
(iii) D is a male doctor.
(iv) Two persons belonging to the same profession do not travel in the same vehicle.
(v) A is not an engineer and travels in a Creta.
(vi) The pair of sisters A and F travels in the same vehicle.
Which of the following represents the three teachers?
We are given several facts about the passengers and their professions. Let's break it down:
Step 1: Assign professions and vehicles.
B (male engineer) and G (teacher) travel in the Swift.
C is a lady doctor and does not travel with A and F (the sisters).
D is a male doctor.
A and F (the sisters) travel together in the same vehicle, the Creta.
A is not an engineer.
Step 2: Assigning the teachers.
G is already assigned as a teacher (since G travels with B).
The other teachers must be A and E, since they fit the remaining criteria.
Thus, the three teachers are G, E, A. Therefore, the correct answer is: \[ \boxed{GEA}. \]

Two players \( A \) and \( B \) are playing a game. Player \( A \) has two available actions \( a_1 \) and \( a_2 \). Player \( B \) has two available actions \( b_1 \) and \( b_2 \). The payoff matrix arising from their actions is presented below:

Let \( p \) be the probability that player \( A \) plays action \( a_1 \) in the mixed strategy Nash equilibrium of the game.
Then the value of p is (round off to one decimal place).
Three friends, P, Q, and R, are solving a puzzle with statements:
(i) If P is a knight, Q is a knave.
(ii) If Q is a knight, R is a spy.
(iii) If R is a knight, P is a knave. Knights always tell the truth, knaves always lie, and spies sometimes tell the truth. If each friend is either a knight, knave, or spy, who is the knight?
Consider the following statements followed by two conclusions.
Statements: 1. Some men are great. 2. Some men are wise.
Conclusions: 1. Men are either great or wise. 2. Some men are neither great nor wise. Choose the correct option: