Let σ3 = nh 0 0 0 i , h 0 0 1 i , . . , h 1 1 1 io . here, σ3 contains all columns of 0s and 1s of height two.1 . in this setting, a string of symbols in σ3 gives three rows of 0s and 1s. consider each row to be a binary number and let b = {w ∈ σ ∗ 3 |the bottom row of w is the sum of the top two rows}. for example, h 0 0 1 i h 1 0 0 i h 1 1 0 i ∈ b but h 0 0 1 i h 1 0 1 i ∈/ b. show that b is regular by providing a dfa that recognizes it.