Abdur Rehman Usmani
Saturday, 9 January 2016
Thursday, 19 November 2015
Product key to install Windows 10
When you’re asked to enter a product key, please enter one of the following keys depending on the edition of Windows 10 you’re installing or activating.Windows 10 Home: TX9XD-98N7V-6WMQ6-BX7FG-H8Q99
Windows 10 Pro: VK7JG-NPHTM-C97JM-9MPGT-3V66T
Windows 10 Enterprise: NPPR9-FWDCX-D2C8J-H872K-2YT43
These product keys can be used to activate all preview builds of Windows 10 that are officially released by Microsoft, which also means that the key might not work on leaked Windows 10 builds!
Note that the above mentioned Windows 10 product keys work irrespective of the architecture of Windows 10, meaning they support both 32-bit and 64-bit. Just make sure that you’ve typed the 25-character correctly, without any mistakes. Note that all these Windows 10 product keys are offered by Microsoft.
Saturday, 14 November 2015
Wednesday, 21 October 2015
Thursday, 15 October 2015
IDM KEY
Idm key first install IDM version then upgrade that version and then follow the below procedure
Note: In order to avoid any interruption disable you antivirus software for a moment
•Now open IDM and click on registration button a dialogue box will appear
•Enter your name, email address and in serial number option enter one of the following keys
RLDGN-OV9WU-5W589-6VZH1
HUDWE-UO689-6D27B-YM28M
UK3DV-E0MNW-MLQYX-GENA1
398ND-QNAGY-CMMZU-ZPI39
GZLJY-X50S3-0S20D-NFRF9
W3J5U-8U66N-D0B9M-54SLM
EC0Q6-QN7UH-5S3JB-YZMEK
UVQW0-X54FE-QW35Q-SNZF5
FJJTJ-J0FLF-QCVBK-A287M
Note: In order to avoid any interruption disable you antivirus software for a moment
•Now open IDM and click on registration button a dialogue box will appear
•Enter your name, email address and in serial number option enter one of the following keys
RLDGN-OV9WU-5W589-6VZH1
HUDWE-UO689-6D27B-YM28M
UK3DV-E0MNW-MLQYX-GENA1
398ND-QNAGY-CMMZU-ZPI39
GZLJY-X50S3-0S20D-NFRF9
W3J5U-8U66N-D0B9M-54SLM
EC0Q6-QN7UH-5S3JB-YZMEK
UVQW0-X54FE-QW35Q-SNZF5
FJJTJ-J0FLF-QCVBK-A287M
You will see a registration update notice after successful registration of IDM full version
You have done it! Now enjoy IDM for life time share you experience or issues in the comment section below.
You have done it! Now enjoy IDM for life time share you experience or issues in the comment section below.
Wednesday, 1 July 2015
Sunday, 28 June 2015
Discrete Structure
Question
# 37
In the back of an old cupboard you discover a note signed by
a pirate famous for his bizarre sense of humor and love of logical puzzles. In
the note he wrote that he had hidden treasure somewhere on the property. He
listed five true statements (a–e below) and challenged the reader to use them to
figure out the location of the treasure.
a. If this house is next to a lake, then the treasure is not
in the kitchen.
b. If the tree in the front yard is an elm, then the treasure
is in the kitchen.
c. This house is next to a lake.
d. The tree in the front yard is an elm or the treasure is
buried under the flagpole.
e. If the tree in the back yard is an oak, then the treasure
is in the garage. Where is the treasure hidden?
Solution
p=this house is next
to a lake.
q=treasure is not in
the kitchen.
r=tree in the front
yard is an elm.
s= treasure is buried under the
flagpole.
t= tree in the back yard is an oak.
u= the treasure is in the garage.
(p → q) → (1)
(r → ¬q) → (2)
(p) → (3)
(r V s) → (4)
(t → u) → (5)
(p → q)
(p)
∴q → (6) (From 1&3 by using modus ponens)
(r → ¬q)
(q)
∴¬r → (7) (From 2&6 by using modus tollens)
(r V s)
(¬r)
∴s →(8) (From 4&7 by using
elimination)
Hence:-
Treasure is
buried under the flagpole.
Question # 39
The famous detective
Percule Hoirot was called in to solve a baffling murder mystery. He determined
the following facts:
a. Lord Hazelton, the
murdered man, was killed by a blow on the head with a brass candlestick.
b. Either Lady
Hazelton or a maid, Sara, was in the dining room at the time of the murder.
c. If the cook was in
the kitchen at the time of the murder, then the butler killed Lord Hazelton
with a fatal dose of strychnine.
d. If Lady Hazelton
was in the dining room at the time of the murder, then the chauffeur killed
Lord Hazelton.
e. If the cook was not
in the kitchen at the time of the murder, then Sara was not in the dining room
when the murder was committed.
f. If Sara was in the
dining room at the time the murder was committed, then the wine steward killed
Lord Hazelton.
Is it possible for the detective to deduce the
identity of the murderer from these facts? If so, who did murder Lord Hazelton?
(Assume there was only one cause of death.)
Solution
p= Lord Hazelton, the
murdered man, was killed by a blow on the
head with a brass candlestick.
q=Lady Hazelton was in
the dining room at the time of the murder.
r= Sara, was in the
dining room at the time of the murder.
s= the cook was in the
kitchen at the time of the murder.
t= the butler killed
Lord Hazelton with a fatal dose of strychnine.
u=the chauffeur killed
Lord Hazelton.
v= the wine steward
killed Lord Hazelton.
(p) → (1)
(q V r) → (2)
(s → t) → (3)
(q → u) → (4)
(¬s → ¬r) → (5)
(r → v) → (6)
Suppose that the cook was
in the kitchen at the time of murder. Therefore:- (s) → (7)
(s)
(s → t)
∴t → (8) (from 7&3 by using modus
ponens).
∴We have a contradiction that Lord Hazelton was
killed by strychnine and a below on the head. (From 1&8).
∴Supposition that the cook was in
the kitchen at the time of murder is false (by contradiction rule).
∴The cook was not in the kitchen at
the time of murder. (Negation of Supposition).
∴¬s → (9)
(¬s → ¬r)
∴¬r → (10) (From 5&9 by using modus ponens).
(q V r)
∴q → (11) (From 2&10 by using
elimination).
(q → u)
∴u → (12) (From 4&11 by using modus
ponens).
Hence:-
The
chauffeur killed Lord Hazelton.
Question
# 40
Sharky, a leader of
the underworld, was killed by one of his own band of four henchmen. Detective
Sharp interviewed the men and determined that all were lying except for one. He
deduced who killed Sharky on the basis of the following statements:
a. Socko: Lefty killed
Sharky.
b. Fats: Muscles
didn’t kill Sharky.
c. Lefty: Muscles was
shooting craps with Socko when Sharky was knocked off.
d. Muscles: Lefty
didn’t kill Sharky.
Who did kill Sharky.
Solution
p= Lefty killed
Sharky. → (1)
q= Muscles didn’t kill
Sharky. → (2)
If muscles didn’t kill
sharky then lefty killed sharky.
(q → p) → (3) (From 1&2).
As we know that Lefty didn’t kill the sharky. (From c). It
can be written as:-
(¬p) → (4)
Now we slove the equation as follows:-
(q → p)
(¬p)
∴¬ q → (5) (from 3&4 by using modus tollens).
Hence:-
Muscles killed Sharky.
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