Final answer:
The set T = {January, June, July} can be represented in set builder notation based on different characteristics. It can be a set of months in a year or a set of summer months. It cannot fully be a set of months with 31 days or a set of vowels.
Step-by-step explanation:
In set builder notation, the set T = {January, June, July} can be defined according to different characteristics of its elements:
- a) x is a month of the year : Since January, June and July are all months in a year, this set accurately represents T.
- b) x is a summer month : This set also represents T accurately if we're considering the Northern Hemisphere, as June and July are summer months.
- c) x : January and July fit into this category, but June, which has 30 days, does not.
- d) x : This set would not include any elements of set T as none of these are classified as vowels.
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