Answer:
For any string, we use 
Explanation:
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
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 , 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.
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Answer:
(a) 
(b) 
Explanation:
(a)
Volume, V of unit cell
Number of unit cells, N
Where 
is weight of material and 
is density of material
(b)
Number of atoms in paper clip
This is a product of number of unit cells and number of atoms per cell
Since iron has 2 atoms per cell
Number of atoms of iron=
