let's see here. your diagnosis is, "i think my patient has this diagnosis."
"related to" means, "caused by/because he has this disease, condition, or pathology." yes, you may use a medical diagnosis as part of your rationale. however, you can never use a medical diagnosis alone for a nursing diagnosis-- you need your own assessment data for that (in this case, assessment data have been given to you).
"as evidenced by" means, "these are the symptoms i observed/can document from the chart that support my decision." they are the evidence that your diagnosis is correct.
so, let's see if we can neaten this up for you.
based on this information i grouped the significant symptoms and with the help of my nursing diagnosis handbook, came up with the possible diagnoses of ineffective airway clearance,impaired gas exchange, and ineffective breathing patterns. after that i am asked to give a complete diagnosis with the "related to" and "aeb". i can not decide whether to use impaired gas exchange r/t ventilation-perfusion inequality aeb abnormal breathing, cyanosis, tachycardia, hypoxemia, and dyspnea,
"i think my patient has impaired gas exchange because he is having a copd exacerbation. i know this because he is breathing rapidly, but has a very low peripheral oxygen saturation despite oxygen supplementation via venturi mask (indicates poor oxygen transport across the alveolar membrane), central (oral) and peripheral cyanosis (ditto), wheezing (indicating tight/restricted airways, from copd and repeated infection), tachycardia (from low o2), and dyspnea (from tight chest, increased work of breathing with no real result)." (all signs of poor oxygenation d/t lousy alveoli)(do not say "lousy" in your homework :d)
does that make sense?
or ineffective airway clearance r/t hyperplasia of the bronchial walls and asthma aeb adventitous breath sounds, cyanosis, and dyspnea.
i think my patient has ineffective airway clearance, because he has a history of respiratory infections and signs of current infection. i know this because .... well, what do you make of this one? my nanda-i 2012-2014 says the defining characteristics of this nursing diagnosis can include absent cough, adventitious sounds, change in rate and rhythm, cyanosis, difficulty talking, dyspnea, excessive sputum, ineffective cough, orthopnea, restlessness, wide-eyed. i will leave it to you to read the related factors, of which he has several, too.
i'm personally leaning towards the first diagnosis, because it's the most serious-- he's already in a deep hole with very low levels of oxygen to support all the hard work he's doing, and he's going to run out of gas (little pun there) and crash really soon.