Question
In: Computer Science
Part #1 Prove the following by using a Truth Table: x + !xy = x +...
Part #1
Prove the following by using a Truth Table:
x + !xy = x + y
Part #2
Prove the following by using a Truth Table:
x(!x + y) = xy
Part #3
Simplify the following Boolean expression using Karnaugh maps:
ABC + ABC + ABC
Part #4
Simplify the following Boolean expression using Karnaugh maps:
ABC + ABC + ABC
Part #5
Simplify the following Boolean expression using Karnaugh maps:
ABCD + ABCD + ABCD + ABCD
Part #6
Simplify the following Boolean expression using Karnaugh maps:
ABCD + ABCD + ABCD + ABCD
Solutions
Expert Solution
Part #1
Prove the following by using a Truth Table:
x + !xy = x + y
x + !xy = x + y
x + !xy
|
x |
y |
!x |
!xy |
x+!xy |
|
F |
F |
T |
F |
F |
|
F |
T |
T |
T |
T |
|
T |
F |
F |
F |
T |
|
T |
T |
F |
F |
T |
x + y
|
x |
y |
x +y |
|
F |
F |
F |
|
F |
T |
T |
|
T |
F |
T |
|
T |
T |
T |
see the results of the both of the truth table
hence, it is proved
---
Part #2
Prove the following by using a Truth Table:
x(!x + y) = xy
x(!x + y) = xy
x(!x + y)
|
x |
y |
!x |
!x +y |
x(!x + y) |
|
F |
F |
T |
T |
F |
|
F |
T |
T |
T |
F |
|
T |
F |
F |
F |
F |
|
T |
T |
F |
T |
T |
xy
|
x |
y |
xy |
|
F |
F |
F |
|
F |
T |
F |
|
T |
F |
F |
|
T |
T |
T |
see the results of the both of the truth table
hence, it is proved
---
solved part 1 and part 2
please post part 3, 4,5 & 6 correctly
see the questions repeated expression
(for example it will be ABC +A'BC+AB'C)
the complement part is missing
please post it correctly, love to answer
all the best
please upvote
venereology answered 11 months agoRelated Solutions
2. Prove the following properties. (b) Prove that x + ¯ xy = x + y.
2. Prove the following properties.(b) Prove that x + ¯ xy = x + y.3. Consider the following Boolean function: F = x¯ y + xy¯ z +
xyz(a) Draw a circuit diagram to obtain the output F. (b) Use the
Boolean algebra theorems to simplify the output function F into the
minimum number of input literals.
1. write a truth table using this symbol: --> 2. write the inputs for the truth...
1. write a truth table using this symbol: -->
2. write the inputs for the truth table to the left of the
--> and write the outputs for the truth table to the right of
the -->
3. write the compliment, or NOT using '
As an example:
The truth table for AND is written this way:
A B --> A AND B
0 0 --> 0
0 1 --> 0
1 0 --> 0
1 1 --> 1
or...
1. write a truth table using this symbol: --> 2. write the inputs for the truth...
1. write a truth table using this symbol: -->
2. write the inputs for the truth table to the left of the
--> and write the outputs for the truth table to the right of
the -->
3. write the compliment, or NOT using '
As an example:
The truth table for AND is written this way:
A B --> A AND B
0 0 --> 0
0 1 --> 0
1 0 --> 0
1 1 --> 1
or...
Prove or disprove using a Truth Table( De Morgan's Law) ¬(p∧q) ≡ ¬p∨¬q
Prove or disprove using a Truth Table( De Morgan's Law) ¬(p∧q) ≡ ¬p∨¬q Show the Truth Table for (p∨r) (r→¬q)
Using the following data... (a) Fill in the table: X Y X2 Y2 XY 8 5...
Using the following data...
(a) Fill in the table:
X
Y
X2
Y2
XY
8
5
4
3
9
7
7
6
5
6
ΣX =
ΣY =
ΣX2 =
ΣY2 =
ΣXY =
(b) Compute the degrees of freedom and determine the critical value
of r for α = 0.05 (two-tails).
df =
r-critical =
(c) Compute SSX, SSY,
SP, and the Pearson correlation (r). (Use 3
decimals)
SSX =
SSY =
SP =
r =
(d) What decision...
Using the following data... (a) Fill in the table: X Y X2 Y2 XY 5 2...
Using the following data...
(a) Fill in the table:
X
Y
X2
Y2
XY
5
2
7
3
10
4
8
5
7
4
ΣX =
ΣY =
ΣX2 =
ΣY2 =
ΣXY =
(b) Compute the degrees of freedom and determine the critical value
of r for α = 0.05 (two-tails).
df =
r-critical =
(c) Compute SSX, SSY,
SP, and the Pearson correlation (r). (Use 3
decimals)
SSX =
SSY =
SP =
r =
(d) What decision...
Answer the following questions: (a) Show that the following is a tautology by using truth table...
Answer the following questions: (a) Show that the following is a
tautology by using truth table and using list of equivalences.
(This problem should be solved using 2 different methods mentioned
above). ((¬p −→ q) ∧ (¬p −→ ¬q)) −→ p (b) Show that the compound
propositions are logically equivalent, by using truth table and
using list of equivalences. ¬p ∨ (r −→ ¬q) and (¬p ∨ ¬q) ∨ ¬r (c)
Show that the propositions ¬p ∨ (¬r ∨ q)...
Determine whether each statement is true or false, and prove or disprove, as appropriate. (a) (∀x∈R)(∃y∈R)[xy=1].(∀x∈R)(∃y∈R)[xy=1]....
Determine whether each statement is true or false, and prove or
disprove, as appropriate.
(a) (∀x∈R)(∃y∈R)[xy=1].(∀x∈R)(∃y∈R)[xy=1].
(b) (∃x∈R)(∀y∈R)[xy=1].(∃x∈R)(∀y∈R)[xy=1].
(c) (∃x∈R)(∀y∈R)[xy>0].(∃x∈R)(∀y∈R)[xy>0].
(d) (∀x∈R)(∃y∈R)[xy>0].(∀x∈R)(∃y∈R)[xy>0].
(e) (∀x∈R)(∃y∈R)(∀z∈R)[xy=xz].(∀x∈R)(∃y∈R)(∀z∈R)[xy=xz].
(f) (∃y∈R)(∀x∈R)(∃z∈R)[xy=xz].(∃y∈R)(∀x∈R)(∃z∈R)[xy=xz].
(g) (∀x∈Q)(∃y∈Z)[xy∈Z].(∀x∈Q)(∃y∈Z)[xy∈Z].
(h) (∃x∈Z+)(∀y∈Z+)[y≤x].(∃x∈Z+)(∀y∈Z+)[y≤x].
(i) (∀y∈Z+)(∃x∈Z+)[y≤x].(∀y∈Z+)(∃x∈Z+)[y≤x].
(j)
(∀x,y∈Z)[x<y⇒(∃z∈Z)[x<z<y]].(∀x,y∈Z)[x<y⇒(∃z∈Z)[x<z<y]].
(k)
(∀x,y∈Q)[x<y⇒(∃z∈Q)[x<z<y]].(∀x,y∈Q)[x<y⇒(∃z∈Q)[x<z<y]].
Prove the following equivalences without using truth tables, and specify at each step of your proof...
Prove the following equivalences without using truth tables, and
specify at each step of your proof the equivalence law you are
using.
(a) ¬ (p ∨ (¬ p ∧ q)) ≡ ¬ p ∧ ¬ q
(b) ( x → y) ∧ ( x → z) ≡ x → ( y ∧ z)
(c) (q → (p → r)) ≡ (p → (q → r))
(d) ( Q → P) ∧ ( ¬Q → P) ≡ P
Symbolize the following arguments then check for validity using a truth table. To simplify, leave the...
Symbolize the following arguments then check for validity
using a truth table. To simplify, leave the
parenthetical parts out of your symbolization. All of the
arguments are based loosely on arguments in Chapter One of The
Branded Mind by Eric Du Plessis.
A.(The primary function of emotions is to direct attention, so)
If your client’s purchase was motivated by emotion then it was
related to attention. Your client’s purchase was (motivated by a
desire for well-being or cultural acceptance and...
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