Prove that $||a|-|b||$ is smaller or equal to $|a-b|$
3820
Prove that $||x|-|y||\le |x-y|$
29679
Prove: $|x-y|\leq |x|+|y|$
23869
Prove the implication "if $ac>bc$ and $c>0$, then $a>b$" using the contrapositive
155545
Showing that $a \mid b$ and $b \mid a$ if and only if $a= \pm b$.
155579
Show that $End_A(A)$ = {$r_a$ | $a ∈ A$}
39708
Proving $(A\le B)\vee (B\le A)$ for sets $A$ and $B$
11168
Proof of divisibility: if $a|b$ and $a|(b+c)$ then $a|c$
136304
Prove: $2^b-1\mid{}2^a-1 \iff b\mid{}a$
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
257
Prove that : $m_{a}m_{b}m_{c}\leq\frac{Rs^{2}}{2}$
31465
Prove that if $a \mid b$ then $\gcd(a,b) = |a|$
56351
Prove that these statements $(A \lor \neg B)$ and $\neg A \to \neg B$ are logically equivalent
5369
Proving the inequality $|a-b| \leq |a-c| + |c-b|$ for real $a,b,c$
153823
$|\text{rank}A-\text{rank}B|\leq \text{rank}(A+B)$
64586
How to prove that $\neg((A\cap B)\cup (\neg A \cap C)) = (A\cap\neg B)\cup (\neg A\cap \neg C)$
63535
Prove that if $A – C = B – C$ and $A\cap C = B\cap C$ then $A = B$
122326
Proving $|P(A\cap B)-P(A)P(B)|\leq \frac{1}4$