1. Some football players play cricket.

2. All cricket players play hockey.

Among the options given below, the statement that logically follows from the two statements 1 and 2 above, is:

Football Players and Logical Deduction

The question presents two statements about sports players and asks us to identify the logical conclusion that follows from them. This type of problem tests our ability to apply deductive reasoning and understand the relationships between different groups of players.

Analyzing the Player Statements

Let's carefully examine the two given statements, focusing on the groups of football players, cricket players, and hockey players:

- Statement 1: Some football players play cricket.
- Statement 2: All cricket players play hockey.

To understand the logical flow, let's break down each statement individually:

- "Some football players play cricket": This statement signifies that there is an overlap between the group of football players and the group of cricket players. It means that at least one, and possibly many, individuals are members of both groups. It does not imply that all football players play cricket, nor does it mean that all cricket players play football.
- "All cricket players play hockey": This is a universal statement. It establishes a complete inclusion: every single person who plays cricket is also a hockey player. There are no exceptions within the group of cricket players regarding their participation in hockey.

Connecting Football and Hockey Players

Now, let's combine the information from both statements to find a logical connection between football players and hockey players. This process is a form of logical deduction, similar to a syllogism.

From Statement 1, we identify a specific subgroup of individuals: those who are both football players and cricket players. Let's imagine this subgroup for a moment.

From Statement 2, we know a crucial rule: every single cricket player also plays hockey. Since the subgroup we identified from Statement 1 (the football players who play cricket) consists of cricket players, they must, by definition of Statement 2, also be hockey players.

Therefore, the individuals who are both football players and cricket players are necessarily also hockey players. This means that there exists at least one individual who is a football player and also a hockey player.

We can represent this using set notation:

- Let $F$ be the set of football players.
- Let $C$ be the set of cricket players.
- Let $H$ be the set of hockey players.

Statement 1 implies: $F\cap C\ne \varnothing$ (The intersection of the set of football players and cricket players is not empty).
Statement 2 implies: $C\subseteq H$ (The set of cricket players is a subset of the set of hockey players).

If there is an element $x$ such that $x\in F$ and $x\in C$ (from Statement 1), and since all elements of $C$ are also in $H$ (from Statement 2), then that same element $x$ must also be in $H$. Consequently, $x\in F$ and $x\in H$, which means $F\cap H\ne \varnothing$.

This directly leads to the logical conclusion: Some football players play hockey.

Evaluating the Options for Logical Conclusion

Let's examine each given option and determine whether it logically follows from the two original statements:Based on our detailed analysis and logical deduction, the only statement that logically follows from the two given statements is that Some football players play hockey.