Math Problem Statement

Let U = {p, q, r, s, t}, D = {p, r, s, t}, E = {q, s}, F = {t, 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. For this to be true, every element in set FF must also be an element in set DD.

Given:

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

Now, let's check if all elements of FF are in DD:

  • tt is in DD
  • ss is in DD

Since both elements of FF are in DD, it follows that FDF \subset D is true.

Would you like more details or have any other questions?

Here are 5 related questions to consider:

  1. What is the definition of a proper subset?
  2. Is GFG \subset F true or false, given the sets?
  3. What is the union of sets EE and FF?
  4. How do you find the intersection of sets DD and GG?
  5. Is the set UU a superset of FF?

Tip: When determining if one set is a subset of another, carefully check if every element of the smaller set is included in the larger set.

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Math Problem Analysis

Mathematical Concepts

Set Theory
Subsets

Formulas

A ⊂ B if and only if every element of A is also an element of B

Theorems

Subset Theorem

Suitable Grade Level

Grades 6-8