Is $(m \Leftrightarrow m) \Leftrightarrow (m \Rightarrow m)$ a tautology, contradiction or contingent? Is this a Tautology, contradiction or contingent? 
$(m \Leftrightarrow m) \Leftrightarrow (m \Rightarrow m)$
My answer is that It is a tautology. But what is yours?
Can someone please explain with a truth table? 
Thank you so much!!!!!
 A: m  |  m <--> m | m --> m | (m <-> m) <--> (m --> m) 
T  |     T     |    T    |             T            
F  |     T     |    T    |             T   

Note that each of $m \rightarrow m$ and $m \leftrightarrow m$ is a tautology (always true, regardless of the truth value of $m$), and hence, $$(m \leftrightarrow m) \leftrightarrow (m \rightarrow m)$$       
is necessarily a tautology, as well, which means the following equivalence necessarily holds: $$(m \leftrightarrow m) \leftrightarrow (m \rightarrow m) \equiv T$$
A: It is tauntology.
p  q  |  p->q
T  T  |   T
T  F  |   F
F  T  |   T
F  F  |   T

You always have the same value, that is m
$$
(m\implies m)
$$
is always true when the inputs are same.
A: In Polish notation we can prove this from the following axioms under the rule of detachment: 
{C$\alpha$$\beta$, $\alpha$} $\vdash$ $\beta$.  
"C" symbolizes the conditional, and "E" the bi-conditional or equivalence operator.  The well-formed formula has Emm on the left, Cmm on the right, and reads EEmmCmm.
Axiom 1-CmCnm   Recursive Letter Prefixing 
Axiom 2-CCmCnoCCmnCmo  Self-Distribution  
Axiom 3-CCmnCCnmEmn
The notation $\alpha$/$\beta$ indicates that the lower case letter $\alpha$ gets substituted uniformly with the well-formed formula $\beta$.  The numeral symbols refer to the well-formed formulas.  * functions as a separator, and - serves as a sign of detachment.  So, 3 m/n * C2-4 would mean that in well-formed formula 3 we will substitute all instances of "m" with n, it has the same form (it is "the same" well-formed formula) as the well-formed formula as a conditional with 2 as the antecedent, and 4 the consequent.  We will thus detach well-formed formula 4.
  2 o/m * 4

4 CCmCnmCCmnCmm
  4 * C1-5

5 CCmnCmm
  5 n/Cnm * C1-6

6 Cmm
  3 n/m*C6-7

7 CCmmEmm
  7*C6-8

8 Emm
  1 m/Cmm, n/Emm * C6-9

9 CEmmCmm
  3 m/Emm, n/Cmm * C9-10

10 CCCmmEmmEEmmCmm
  10 * C7-11

11 EEmmCmm
