Show that the following languages are regular

(a) {x {0, 1} | x does not contain 101 or |x| is a multiple of 3}.

(b) x {0, 1} [#0(x) #1(x) is not a multiple of 3] and [bin(x) is a multiple of 3]

Here #b(x) denotes the number of bs in x

(c) {x {a, b, c} | x begins with cab, does not contain aa, and ends with bab}.

(d) {x {a, b, c} | x uses at most two different symbols}. (e) {x {a, b} | the third symbol of x equals the third from last symbol of x}. (f) {x {0, 1} | the third from last bit of x equals the parity of x}. The parity of x is 1 if #1(x) is odd, 0 if #1(x) is even.