Let $A,\,B$ be subsets of the set $X$. Prove one of de Morgan's Laws of Set Theory
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De Morgan's laws in logic and set theory
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Proof of A ⊆ C and B ⊆ C ⇔ A ∪ B ⊆ C
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Let $ A $, $ B $ and $ C $ be sets. If $ A \cup B = A \cup C $ and $ A \cap B = A \cap C $, then show that $ B = C $.
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ZF Set Theory - If $|A|^{|B|} = |B|$, then $|A| = 1 = |B|.$
52135
Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$
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Proof of Sets involving the Cartesian Product
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Expressing $\Bbb N$ as an infinite union of disjoint infinite subsets.
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Proving $(A\times C)\cup(B\times D)\subseteq(A\cup B)\times(C\cup D)$
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(exercise from Tao's analysis book) Proof of a lemma relating to power set of X
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Double Complement of a set proof
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Proving that $A+A \not\subset 2A $ using a particular definition for sum of sets
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Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.
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Subset of a finite set is finite
112084
Proof of a formula for the power set of a union of two sets
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Let $A$ be a finite set and let $B$ be a subset of $A$ with $|A|=n$,$|B|=m$ and $0<m<n$. Count the subsets of $A$ containing $ B.$
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Let $A$ be a nonempty subset of $\mathbb{R}$. Prove...
6098
Let $f:A\rightarrow B$ and $C\subset B,D\subset B$. Prove that $f^{-1}(C\backslash D)=f^{-1}(C)\backslash f^{-1}(D)$