Could you further clarify how the union of a family set consisting of just {∅} becomes ∅?
From my previous example, what would ∪F be?
Family of sets F = {{1,2,3},{4,5,6},{∅}}
∪F = {1, 2, 3, 4, 5, 6} or {∅, 1, 2, 3, 4, 5, 6}?
Just so I understand, an empty set in a family of sets would be the following?:
Family of sets F = {{1,2,3},{4,5,6},{∅}}?
Suppose I included an empty set in both of the families, would the intersection still be a disjoint or would it be the set {∅}?
I can't think of a counterexample to disprove this set theory "theorem"
Assume F and G are families of sets.
IF \cupF \bigcap \cupG = ∅ (disjoint), THEN F \bigcap G are disjoint as well.
Hello,
Thank you all for helping me with this. I am only self-learning basic logic from a book, and the author never worked out distribution of all of the content in the parentheses to another, so I only thought you could distribute one letter at a time.
I have a new problem:
Prove (P...
show that P \leftrightarrow Q is equal to (P\wedgeQ) \vee (\negP \wedge\negQ)
(P→Q) \wedge (Q→P)
(\negP\veeQ) \wedge (\negQ\veeP)
[\neg(P\wedge\negQ)\wedge\neg(Q\wedge\negP)]
\neg[(P\wedge\negQ)\vee(Q\wedge\negP)]
I don't know which law to use from this point on to prove the...