Is it correct to say "A deterioration in my grandfather's health and memory has just begun"?. Or is it began?
Begun is correct. Began is past tense. Begun this the past participle, so "has begun" is correct. :)
"I Have Not Yet Begun to Fight," 1779 John Paul Jones http://www.eyewitnesstohistory.com/johnpauljones.htm
"We Have Only Just Begun to Fight". Franklin Roosevelt. October 31, 1936. https://patriotpost.us/documents/284
The correct word to use in this sentence is "has just begun."
Here's an explanation of why "has just begun" is the correct choice:
The word "deterioration" is a noun, representing the process of becoming progressively worse. In this sentence, "deterioration" is the subject of the sentence, and it is singular.
The verb form that agrees with the singular subject "deterioration" is "has." This is the present perfect tense of the verb "to have." The present perfect tense is formed using the auxiliary verb "have" or "has" and the past participle of the main verb.
In this case, the past participle of the main verb "begin" is "begun." Therefore, the correct form is "has just begun."
To determine the correct verb form in sentences like this, it can be helpful to break down the main subject and verb and consider their agreement.
In this case:
Subject: A deterioration in my grandfather's health and memory
Verb: has just begun
So, putting it all together, the correct sentence is: "A deterioration in my grandfather's health and memory has just begun."