Could some one please help me to solve this bolean expression.
I want to use it to draw AND, XNOR, NAND, and OR gates + two inverters.
F(a,b,c) = [ab' (+) (a'b)']' + c

What do you mean by solve?

Anyway what you have is:

F(a,b,c) = XNOR(a,b) OR c

So you want to use F(a,b,c) to make AND(a,b), XNOR(a,b), etc?

Well making XNOR is easy, you just set c to 0. You should probably work the rest by yourself, though.

I misread your post and didn't see that tick next to (a'b). I also didn't realize that you are using (+) to denote xor. . . whoops.

So F(a,b,c) isn't as I described (isn't just xnor(blah) or c).

Simplifies as:
F(a,b,c) = [ab' (+) (a'b)']' + c
= [ab' (+) (a + b')]' + c

Off the top of my head I don't know how to simplify the expression in [] as a function of a and b.

But you can just try all 4 pairs to produce a truth table. From that you'll be able to figure out what the inner function is doing.

My truth table looks like this:
a | b| [ab' (+) (a'b)']'
0 | 0 | 0
0 | 1 | 0
1 | 0 | 1
1| 1  | 0

If this table is correct (which you'll need to double check), then this tells us that

[ab' (+) (a'b)']' = ab'

So F(a,b,c) = ab' OR C.

Anyway from this you should be good to go. . . hopefully you see the general pattern for solving these problems.

Again, double check that I haven't made any mistakes here and am interpreting your question properly.