Answer :
The maximal elements of the poset ({3, 5, 9, 15, 24, 45}, |) are 24 and 45, as they are not divisible by any other element in the set.Hence, the maximal elements of the poset are 24 and 45.
The question asks us to find the maximal elements in the poset consisting of the set {3, 5, 9, 15, 24, 45} with the divisibility relation '|'. In a poset, a maximal element is an element that is not divisible by any other element in the set. Analyzing the given set, we can see that:
- 3 is divided by 9, 15, and 45
- 5 is divided by 15 and 45
- 9 is divided by 45
- 15 is divided by 45
- 24 has no divisors in the set, so 24 is a maximal element
- 45 has no divisors in the set, so 45 is also a maximal element
Hence, the maximal elements of the poset are 24 and 45.
