Let A,B,C be sets. Prove that A−(B−C)=(A-B)-C
104124
Prove or disprove: $A-(B-C) = (A-B)-C$
124742
P(A|C)=P(A|B)*P(B|C)?
114780
$\forall a,b,c \in \mathbb{N}\!:\ a\mid b \Rightarrow ac\mid bc. $ Divisibility Proof
43068
Let A and B be sets. Show that A is a subset of B if and only if for any set C, one has A union C is a subset of B union C.
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
153670
Prove that if $a \mid b$ and $b \mid c$, then $a \mid c$.
66563
Is $ (A∪B)×(C∩D)=(A∪C)×(B∪D)$ true for all sets A,B,C and D?
136854
Prove: For a,b,c positive integers, ac divides bc if and only if a divides b
88982
Prove that for any two sets $A$ and $B$, $A\notin B$ or $B\notin A$
32253
How to prove $b=c$ if $ab=ac$ (cancellation law in groups)?
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$
51321
Prove that $A = B = C = D$
102133
Prove: $\gcd(a,b) = \gcd(a, b + at)$.
2289
Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
128820
Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$
68258
Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$
81618
Prove $||a|-|b| | \leq |a-b|$