Final answer:
The set E of all even negative integers greater than -20 is expressed in set-builder notation as E = x ∈ ℤ , which includes integers from -18 to -2.
Step-by-step explanation:
The set E of all even negative integers greater than -20 can be written using set-builder notation. Given this definition, the correct notation for E would be E = -20 < x < 0 ∧ x ∠ 2 = 0, where ℤ denotes the set of all integers, ∈ means 'belongs to', -20 < x < 0 indicates that x is greater than -20 and less than 0, ∧ is the logical 'and', x ∠ 2 = 0 ensures that x is even (i.e., divisible by 2), and | is such that.
To explicitly list the members of set E, one would include all the even negative integers from -18 up to -2 (the largest even negative integer less than zero), resulting in E = {-18, -16, -14, -12, -10, -8, -6, -4, -2}.
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