The discussion centers on proving that the intersection of two sets, denoted as (A ∩ B), is a subset of A using simplification from the rule of inference. It is established that the logical rule applies to logical statements rather than directly to sets. The correct approach involves decomposing the statement into logical components, starting with the assumption that x belongs to A ∩ B, leading to the conclusion that x must belong to A.
PREREQUISITESMathematicians, students of discrete mathematics, and anyone interested in understanding set theory and logical proofs will benefit from this discussion.
Sort of--that logical rule applies only to logical statements, not directly to sets. It says that you can conclude X from the statement X AND Y. The standard way to prove that [tex]A \cap B \subseteq A[/tex] starts by decomposing it into logical statements.brad sue said:Hi,
with my special notation:
I- intersection
Can we prove that:
(A I B) subset of A by simplification from the rule of inference
since A I B -->A ??
If not, please can I have some suggestions?
B
0rthodontist said:Sort of--that logical rule applies only to logical statements, not directly to sets. It says that you can conclude X from the statement X AND Y. The standard way to prove that [tex]A \cap B \subseteq A[/tex] starts by decomposing it into logical statements.
Assume [tex]x \in A \cap B[/tex]
Then [tex](x \in A) \vee (x \in B)[/tex]
You can finish it