I think: c+ab
your minterms are {1,3,5,6,7} you can K-map it or Quine mcCluskey you get the simplified form above.
Resulting into:
1 AND
1 OR
your concern when a = 1; your orig equation becomes b+/bc is actually equal to b + c when you take the minterms.
A quick check for the orig and simplified form if they are the same is plug in all possible values of a, b and c; you will get the same result;
if you want to implement it via NAND or NOR gates, you may not get a simplified form.
Thanks,