This is a Discrete Mathematics problem. I need help with the answers to number 16 and number 18.

foo b b d df Prove that B is a Boolean algebra. 13. Use the axioms to prove the third and fourth distributive law 14. Use the axioms to prove de Morgan's Laws (Theorem 18) In Exercises 15 to 18, prove that the results hold in any Boolean a 15,x+x,y = x + y for any x and y. 16. x + xy + y = (x + y)(y + 1) for any x and y. 17. (x + y')z' = ((x' + z) (y + z)), for any x, y and z. hold in any 18. x + y(x + z) = (x + y)(x + z) for any x, y and z. 19. Write down the duals of the equations in Exercises 15 to 18. 20. Prove that, in any Boolean algebra, x + y + x,y,z = x + y + z and z. 21. Suppose the elements x, y, and z in a Boolean algebra satisfyx Prove that x' = yz + y ,z