Using KMap minimize the function: f(x, y, z) = ∑ (0, 2, 5, 7) +
d(3,...
Using KMap minimize the function: f(x, y, z) = ∑ (0, 2, 5, 7) +
d(3, 4, 6)
Do not use Boolean algebra. Use KMaps.
For the 3CNF
f = (x’ +y’+z)& (x+y’+z’)&(x+y+z’)&
(x’+y+z)&(x’+y+z’) &(x+y+z)
where “+” is or, “&” is...
For the 3CNF
f = (x’ +y’+z)& (x+y’+z’)&(x+y+z’)&
(x’+y+z)&(x’+y+z’) &(x+y+z)
where “+” is or, “&” is and operations, “
’ ” is negation.
a)give 01 assignment to variables such that
f=1 x= ______ y= ______ z= ____
f=0 x= ______ y= ______ z= ____

b) Draw the corresponding graph and mark the
maximum independent
set.
(you can draw on paper, scan and insert here)
Prove: Let x,y be in R such that x < y.
There exists a z in...
Prove: Let x,y be in R such that x < y.
There exists a z in R such that x < z <
y.
Given:
Axiom 8.1. For all x,y,z in
R:
(i) x + y = y + x
(ii) (x + y) + z = x + (y + z)
(iii) x*(y + z) = x*y + x*z
(iv) x*y = y*x
(v) (x*y)*z = x*(y*z)
Axiom 8.2. There exists a real number 0 such that
for all...
Determine how the following lines interact.
(x, y, z) = (2, 1, 3) + t(1, 1,...
Determine how the following lines interact.
(x, y, z) = (2, 1, 3) + t(1, 1, 5) ; (x, y, z) =
(3, 0, 2) + s(1, 2, 3)
(x, y, z) = (1, 2, 0) + t(1, 1, 1) ; (x, y, z) =
(3, 4, 1) + s(2, 2, 2)
x = 2 + t, y = 1 + 2t, z = 1 – t ; x = 1  2s,
y = 1 1s, z = 1...
Solve
a. x + y + z = 2, x – y + z = 3,
x...
Solve
a. x + y + z = 2, x – y + z = 3,
x + y + 2z = 0
b. 5x + y – 2z = 2, x + 2y + 3z
= 2, 2x – y = 3
Prove or disprove following by giving examples:
(a) If X ⊂ Y and X ⊂ Z,...
Prove or disprove following by giving examples:
(a) If X ⊂ Y and X ⊂ Z, then X ⊂ Y ∩ Z
(b) If X ⊆ Y and Y ⊆ Z, then X ⊆ Z
(c) If X ∈ Y and Y ∈ Z, then X ∈ Z