1. Evaluate the boolean expression x(yz' + y'z) at the ordered triplets
(1, 0, 1) and (1, 1, 1).
2. Evaluate the boolean expression (x + y + z)(x + y' + z).
3. How many constant boolean functions can be defined from B n to B,
with B a two-element boolean algebra?
4. Find the number of boolean functions that can be defined from B n to B, where B is a two-element boolean algebra.
Determine if each is a boolean expression, where each variable is boolean.
5. ((xy')')' 6. x' + yz 7. (xy + y'z')' 8. x(yz')'
Construct a logic table for each boolean function defined by each boolean
expression.
9. (x + y')(x' + y)
11. xy + y~z + yz ~
13. (x + y' + z)(xy'z)
15. xyz + x(yz)'
Using a logic table, verify each.
17. x + xy = x 18. x(x + y) = x
21. (x +y)' ~: x' +y'
10. x (y' z + yz' )
12. (x + y' + z)(x' + y + z')
14. xyz + (xyz)'
16. x'yz' + x' (yz)'
19. (x+y)' = x'y'
22. (xy)' r x'y'
20. (xy)' = x' +y'
23. Is the equality relation on the set of boolean expressions in n variables
an equivalence relation?