Given : A and B are input terminals.
Logic $1=>5V$
Logic $0=<1V$
Which logic gate operation, the following circuit does?

Since, when A and B both are logic 1 then no current will flow through the both  $50\Omega$
resistors, because both the diodes will not conduct. therefore, whole current will flow through $R=10K$
and output is potential difference across the $R=10K$ which will be $6V$ in this case means high 
Now, When either of the input is low current through terminal which is low will flow through it and most of the current will flow through the $50\Omega$ resistance since it is very very less than $R=10K$ therefore, Potential across $R=10K$ will be less than $1V$ . Hence, when either of input is low output is also low.
When both the inputs are low same case as when either of input is low will be there hence output will also be low.
Therefore, above circuit acts as a AND Logic gate.