In set theory, when we say "P = {1, 2, 3, 4}," we're simply stating that P is a set that contains the elements 1, 2, 3, and 4. A set is a collection of distinct objects, considered as an object in its own right. Sets are typically denoted by curly braces {}, and the elements within those braces are the members of the set.
Given that U is the universal set, which in your case is U = {1, 2, 3, 4, 5, 6, 7, 8}, and P is defined to be a subset of U, P will contain elements that are also present in U.
So, when you ask, "What is P?" the answer is that P is the set containing the elements 1, 2, 3, and 4. To be clear:
P = {1, 2, 3, 4}
This means that the set P has four members, and all of these members are also part of the universal set U.
In terms of set membership, we could also say that:
- 1 ∈ P (1 is a member of P),
- 2 ∈ P (2 is a member of P),
- 3 ∈ P (3 is a member of P), and
- 4 ∈ P (4 is a member of P).
In summary, P is a set with four elements, and those elements are the numbers 1, 2, 3, and 4.