Or gate and And gate.

 Or gate working

A=0,B=0 Both D1 and D2 don't conduct. Hence output y=0

A=0,B=0, D1 conducts D2 does not conduct.hence output y=1.

A=1,B=0  D1 conducts,D2 does not conduct. Hence output y=1 .

A=1,B=1, Both  D1 and D2 conduct.

Hence output y=1.

AND gate

It is realised by using two junction diode.

It has two or more inputs but one output.

It is expressed as y=A AND B=A.B (reads as y equals A AND B).

Conclusion

It all input are 1 them output is 1.

Working

If A=0,B=0, Both D1 and D2 are Forward biased and conduct.since both diodes are short circuited, output y=0.

If A=0,B=1,D1 is Forward blased but short circuited. 

Hence output y=0.

If A=1,B=0,D1 does not conduct. D2 is Forward biased but short circuited . Hence output y=0.