Math Problem Statement

Let U = {p, q, r, s, t}, D = {p, r, s, t}, E = {q, s}, F = {r, s}, and G = {s}. Determine whether the statement is true or false. F ⊂ D

Solution

The statement FDF \subset D means that set FF is a subset of set DD. A set FF is a subset of another set DD if all elements of FF are also elements of DD.

Let's check this:

  • Set F={r,s}F = \{r, s\}
  • Set D={p,r,s,t}D = \{p, r, s, t\}

Now, look at the elements of FF:

  • Element rr is in DD.
  • Element ss is in DD.

Since all elements of FF are in DD, we can conclude that:

FDF \subset D

Therefore, the statement FDF \subset D is true.

Would you like any further details or have any questions?

Here are 5 related questions to explore:

  1. What is the difference between a subset and a proper subset?
  2. Can a set be a subset of itself?
  3. What does FDF \subseteq D mean, and how is it different from FDF \subset D?
  4. Is the empty set a subset of all sets?
  5. If G={s}G = \{s\}, is GFG \subset F?

Tip: A set is always a subset of itself, but it is only a proper subset if it doesn't contain all elements of the other set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Subsets

Formulas

Subset Definition: A is a subset of B if every element of A is also an element of B.

Theorems

Subset Theorem: A set A is a subset of a set B if every element of A is in B.

Suitable Grade Level

Grades 6-8