Question

Can anyone plz explain me the main concept of mapping reducibility on Turing machine and what the symbols stands for plz

Answer 1

If you mean the computer created by Turnig
dot or no space AND, AB
+ for OR, A+B
these are logic symbol used generally where A, B are binary bits
Having to registers of binary bits one can add with binary addition using the above logic in proper sequence, as half adder or full adder

Answer 2

AB
00=0
01=0
10=1
11=1
A+B
0+0=0
0+1=1
1+0=1
1+1=1