Prove that if $A \mathbin{\triangle} C = B \mathbin{\triangle} C$, then $A = B$
67717
$A \oplus B = A \oplus C$ imply $B = C$?
53660
Show that $ a，b，c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q  \implies  \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $
104124
Prove or disprove: $A-(B-C) = (A-B)-C$
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
123133
If, in a triangle, $\cos(A) + \cos(B) + 2\cos(C) = 2$ prove that the sides of the triangle are in AP
124868
Prove that $\frac{bc}{b+c}+\frac{ca}{c+a}+\frac{ab}{a+b}<\frac{a+b+c}{2}$
80759
Proving $A\times (B\cap C)=(A \times B)\cap (A\times C)$.
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
35242
If $a$, $b$, $c$, $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}$, and $\frac{a}{c}+\frac{b}{a}+\frac{c}{b}$ are all integers, then $|a|=|b|=|c|$
133699
Proving that there is a bijection between $A$ and $B$.
145058
Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
10348
Prove that if the $\gcd(a,b)=1$, then $\gcd(a+b,ab)=1$
151852
How to prove $A \subset B \iff A \cup B = B$
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
127296
prove that a|b and b|a iff a=+-b
113641
Suppose the gcd (a,b) = 1 and c divides a + b. Prove that gcd (a,c) = 1 = gcd (b,c)
104068
Prove that $\forall a,b\in\mathbb{C} \exists c,d \in \mathbb{C}: c+d = a \land cd = b$