The binary number representation of the decimal number $67$ is 

Read the following information carefully and answer the question given below:

Statement :
I. Either he is happy or he is poor.
II. He is happy.
Inference:
He is poor. 

If A and B are Two input gate of and Logic gate and AB is the only output. What will be the output if the input is A = 1 and B = 0?

Consider the operations:

$f(X,Y,Z)=X\text{'}YZ+XY\text{'}+Y\text{'}Z\text{'}$ and $g(X,Y,Z)=X\text{'}YZ+X\text{'}YZ\text{'}+XY$

Which one of the following is correct?