The problem presents four statements, and you need to determine which are true or false.

1. Minden transzpozíció páratlan permutáció.

   • Translation: Every transposition is an odd permutation.
   • True. A transposition is a permutation that swaps two elements, and it is always an odd permutation because it involves an odd number of swaps (1 swap).

2. Egy halmaz önmagára vett bijektív leképezését a halmaz permutációjának nevezzük.

   • Translation: A bijective map from a set to itself is called a permutation of the set.
   • True. By definition, a permutation is a bijective (one-to-one and onto) function from a set to itself.

3. |S₃| = 3.

   • Translation: The order of the symmetric group $S_3$ is 3.
   • False. The symmetric group $S_3$ is the group of all permutations of 3 elements. The order of $S_3$ is $3! = 6$, not 3.

4. Egy páros és egy páratlan permutáció szorzata páratlan.

   • Translation: The product of an even and an odd permutation is odd.
   • False. The product of an even permutation and an odd permutation is always odd. However, this statement claims the wrong result.

Summary:

• 1st: True
• 2nd: True
• 3rd: False
• 4th: False

Would you like more details or have any questions?
Here are 5 related questions:

1. What is a transposition in permutation theory?
2. Can you explain how bijective functions work?
3. How is the order of a symmetric group determined?
4. Why is the product of an odd and even permutation odd?
5. What are some properties of even and odd permutations?

Tip: When dealing with groups like $S_n$, understanding the structure of permutations can help simplify many related problems.