Discrete Mathematics for Computer Science

Exercises 101

(e) -r --*(p A q)

(f) (p -q) - -r

(g) ((p A r) -+ (-q v p)) --* (q v r)

8. Find the expression tree for the following formulas:

(a) (pAq) vr

(b) (p -- q) -- r

(c) p - (q -- r)

9. Find the expression tree for the following formulas:
   (a) -p A (--q v r)
   (b) p v (-q A -r)
   (c) ((p v q) <4 r) * p

(d) (--q A-,r) <-> (p -- (q V r))

10. Find the expression tree for the formula

(p -+ ((-'p) -+ q))

11. Find the expression tree for the formula

((-(p A q)) V (-(q A r))) A ((-(p *-+ (-'(-s)))) V (((r A s) V

12. Find the expression tree for the formula

((((-,(-'p)) A (-q)) A r) V (((-(-,q)) A (-,r)) A s)) +- (s -+ p)

13. Find a boolean expression to represent the following combinatorial circuits:

A

(a)

B

A

B

(b) A

B

C

D

14. Draw a combinatorial circuit for each of the following boolean expressions:

(a) (x A y) V -'Z

(b) (x A y) V (-x A y)

(c) -(-x V y) V (x A Z)

(d) ((x A y) V (y A Z)) V -Z

(e) (x V -(x V y)) V (-x A -y)

15. Find a boolean expression to represent each of the following combinatorial networks
    shown.