Prove that the following wff are valid arguments:

(a) (x) P(x) (x) Q(x) --> (x) [P(x) Q(x)]

(b) (x)[A(x) --> B(x)] --> [(x)A(x) --> (x)B(x)]

(c) (x)[P(x) Q(x)] (y)[Q(y) --> R(y)] --> (x)[P(x) R(x)]

(d) (x) (y)[(P(x) S(x, y)) --> Q(y)] (x) B(x) (x) (B(x) --> P(x)) (x)(y) S(x, y) -->(x) Q(x)