Which logic gate/circuit should be present between a, b & Y?

Question

Thanks for pondering over my question.
Above is a digital logic circuit with 2 inputs, & 1 output. I want following logic to be implemented in sequence :

1. b = 0, a = 0, Y = 0
2. b = 1, a = 0, Y = 1
3. b = 0, a = 1, Y = 1
4. b = 1, a = 1 should be explicitly avoided so that both a & b are not 1 simultaneously
5. Suppose step 3 is tried before step 2, then output should be 0, i.e., Y = 0.

Which logic gate or digital circuit will work for above sequence of logical ops ? I tried with OR and XOR gates, but they don't satisfy condition 5, and sequential operation can't be enforced.
Can I use 2-to-1 priority encoder such as the one shown in figure below ?

Or may be some smart implementation of NOR SR latch ? Please let me know of your thoughts. Thanks ahead of the time.

Answer 1

f XOR a seems to fit perfectly.

How is it that you feel it contradicts condition 1?

a b c F Y
---------
0 0 0 0 0
0 0 1 1 1
0 1 0 1 1
0 1 1 1 1
1 0 0 0 1
1 0 1 1 0
1 1 0 1 0
1 1 1 1 0