johnnyICON
May28-05, 05:56 PM
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?
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?