Midterm Practice: Could some verify my proof

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    Midterm Proof
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SUMMARY

The proof presented demonstrates that if set A is a subset of set B, then the intersection of A and C is a subset of the intersection of B and C. The proof correctly applies the definitions of set intersection and subset relations, confirming that if an element x belongs to both A and C, it must also belong to B, thus establishing the required subset relationship. The logical flow is sound, and no critical elements are missing from the argument.

PREREQUISITES
  • Understanding of set theory concepts, specifically subsets and intersections.
  • Familiarity with formal proof techniques in mathematics.
  • Knowledge of logical reasoning and implications in mathematical statements.
  • Basic notation used in set theory, such as A ⊆ B and A ∩ C.
NEXT STEPS
  • Explore advanced topics in set theory, such as Cartesian products and power sets.
  • Study formal proof techniques, including direct proof and proof by contradiction.
  • Learn about the properties of set operations, including distributive laws.
  • Investigate applications of set theory in computer science, particularly in database management and query optimization.
USEFUL FOR

Students studying mathematics, particularly those focusing on set theory and formal proofs, as well as educators looking for examples of proof verification techniques.

johnnyICON
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Midterm Practice: Could someone verify my proof

A sample question that I tried proving is:

Formally show that [tex]A \subseteq B,~then~A \cap C \subseteq B \cap C[/tex]

My Proof:
Suppose [tex]x \in A \cap C[/tex]. Then by definition of intersection, [tex]x \in A~and~x \in C[/tex]. But as [tex]A \subseteq B,~then~x \in B[/tex]. Hence, [tex]x \in B \cap C[/tex]. And therefore, [tex]A \cap C \subseteq B \cap C[/tex].

Is there anything that I've missed? Is this even right?
 
Last edited:
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It looks fine to me.
 
Hallelujah!
 

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