Question

. What are the results of the following Boolean expressions, such that x- True, y- False, z- False, w True a) x and y b) x and y and z c) xand y and z and w d) xory e) xory or z f) xory or z or w g) (x and y) or (z and w) h) (x ory) and (z or w) i) (notx) or y j) (not x) and (not y) k) not (x or y) l) (not z) or (not w) m) not (z and w) n) xand True o) y or True p) (x and y and z and w) or True

Answer 1

Answer:

Given values of

x=true ,y=false, z=false, w=true

Rules:

1) Value of "(a and b)" will be "true" only all of them are "true" otherwise

it will be "false".

2)Value of "(a or b)" will be "true" if any of them are "true", value will be

"false" when both are "false".

3)"not(x)" will change the value of x. it will be "true" if x is "false" vice

versa.

#part(a):

(x and y)=true and false

(x and y)=false                   (Rule 1.)

#part(b):

(x and y and z) can be written as

((x and y) and z)

put the values in  expression

=((true and false) and false)

=(false and false)                (Rule 1.)

=false                                  (Rule 1.)

#part(c):

(x and y and z and w) can be written as

((x and y) and (z and w))

put the values in  expression

=((true and false) and (false and true)

=(false and false)                      (Rule 1.)

=false                                        (Rule 1.)

#part(d):

(x or y)

put the values in  expression

=(true or false)

=true                             (Rule 2.)

#part(e):

(x or y or z ) can be written as

=((x or y) or z))

put the values in  expression

=((true or false) or false )

=(true or false)                 (Rule 2.)

=true                                (Rule 2.)

#part(f):

(x or y or z or w) can be written as

((x or y) or (z or w))

put the values in  expression

=((true or false) or (false or true)

=(true or true)                  (Rule 2.)

=true                                (Rule 2.)

#part(g):

(x and y) or (z and w)

put the values in  expression

=(true and false) or (false and true)

=false or false                   (Rule 1.)

=false                                (Rule 2.)

#part(h):

(x or y) and (z or w)

put the values in  expression

=(true or false) and (false or true)

=true and true                      (Rule 2.)

=true                                     (Rule 1.)

#part(i):

(not x) or y

put the values in  expression

=(not true) or false

=false or false                     (Rule 3.)

=false                                  (Rule 2.)

#part(j):

(not x) and (not y)

put the values in  expression

=(not true) and (not false)

=false and false                    (Rule 3.)

=false                                    (Rule 1.)

#part(k):

not (x or y)

put the values in  expression

=not(true or false)

=not(true)                          (Rule 2.)

=false                                (Rule 3.)

#part(l):

(not z) or (not w)

put the values in  expression

=(not false) or (not true)

=true or false                      (Rule 3.)

=true                                  (Rule 2.)

#part(m):

not (z and w)

put the values in  expression

=not (false and true)               (Rule 1.)

=not (false)                           (Rule 3.)

=true

#part(n):

x and True

=true and True

=true                               (Rule 1.)

#Part(o):

y or True

=false or True

=true                               (Rule 2.)

#part(p):

(x and y and z and w) or True

=(((x and y) and (z and w)) or True)

put the values in  expression

=(((true and false) and (false and true)) or True)

=((false and false)or True

=false or True

=True