- #1
johnnyICON
- 79
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Midterm Practice: Could someone verify my proof
A sample question that I tried proving is:
Formally show that A \subseteq B,~then~A \cap C \subseteq B \cap C
My Proof:
Suppose x \in A \cap C. Then by definition of intersection, x \in A~and~x \in C. But as A \subseteq B,~then~x \in B. Hence, x \in B \cap C. And therefore, A \cap C \subseteq B \cap C.
Is there anything that I've missed? Is this even right?
A sample question that I tried proving is:
Formally show that A \subseteq B,~then~A \cap C \subseteq B \cap C
My Proof:
Suppose x \in A \cap C. Then by definition of intersection, x \in A~and~x \in C. But as A \subseteq B,~then~x \in B. Hence, x \in B \cap C. And therefore, A \cap C \subseteq B \cap C.
Is there anything that I've missed? Is this even right?
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