The pumping lemma says that for any string s in the language, with length greater than the pumping length p, we can write s = xyz with |xy| ≤ p, such that xyi z is also in the language for every i ≥ 0. For the given language, we can take p = 2.

Here are the cases:

Consider any string a i b j c k in the language. If i = 1 or i > 2, we take $x = \epsilon$ and y = a. If i = 1, we must have j = k and adding any number of a’s still preserves the membership in the language. For i > 2, all strings obtained by pumping y as defined above, have two or more a’s and hence are always in the language.

For i = 2, we can take and y = aa. Since the strings obtained by pumping in this case always have an even number of a’s, they are all in the language.
Finally, for the case i = 0, we take $x = \epsilon$ , and y = b if j > 0 and y = c otherwise. Since strings of the form b j c k are always in the language, we satisfy the conditions of the pumping lemma in this case as well.

8 0

3 years ago

Carbon dioxide steadily flows into a constant pressure heater at 300 K and 100 kPa witha mass flow rate of 9.2 kg/s. Heat transf

docker41 [41]

Answer:

Carbon dioxide temperature at exit is 317.69 K

Carbon dioxide flow rate at heater exit is 20.25 m³/s

Explanation:

Detailed steps are attached below.

8 0

3 years ago

Two technicians are discussing the intake air temperature (IAT) sensor. Technician A says that the computer uses the IAT sensor

mart [117]

Both the technicians are correct.

Explanation

Intake air temperature sensor is used in engines of vehicles to monitor the temperature of air entering the engine.

They are basically made of thermistors whose electrical resistance changes according to temperature.

Depending upon the reading and accuracy of intake air temperature sensor, the power-train control module (PCM) will decide about the air and fuel mixture ratio in the engine.

The hot air in engine requires less fuel to operate the engine parts while cold air requires more fuel to operate the engine.

The ratio of air and fuel mixture should be maintained in the engine and it is done by PCM only after getting the input from IAT. So technician B is saying correct.

Also the IAT works as a backup to support the engine coolant temperature sensor by the computer.

As the IAT checks the temperature of outside air, it will help to change the coolant temperature of the engine based on the environment.

Thus technician A is also correct. So both the technicians are correct.

6 0

3 years ago