1.{0, 1}
Analysis: the representative element is X, and its characteristic is X? =x, and the calculated x is the element X that meets the requirements.
2.{0, 1,2,3,4,5,6,7}
Analysis: Representing an element or X, A can be called a parameter here, through which we can control the value range of the element X. The topic is actually that when A < 50, the number with the root sign can be an integer. For example, when a=9, √9=3=x, 3 is an integer, which meets the requirements of the set, so 3 is an element in this set.
3. a ∩ b = {x | 0 ≤ x <1} a ∪ b = {x |-2 < x <1or 1 < x ≤ 2} (please note that any number is not within the required range and should be deleted).
Analysis: A∩B is a number contained in two sets. Just draw a number axis and see what the common part is.
A∪B is an element of two sets.
4.A∩B={a|a> 1} A∪B={a|a∈(-∞，0)∩( 1/4， 1)∩( 1，+∞)}
Analysis: Set A: The representative element is A, and A meeting the requirements of Set A can make the quadratic equation have a solution, so △≥0 is enough, and the solution is: a∈(-∞, 0)∩( 1, +∞).
Set b: the representative element is also a. If the equation of set b has no solution, △ < 0, the solution is: A > 1/4.
Draw several axes and find out their common parts and * * * parts.
5.A∩B={0}
Set a: y is the representative element. When x is an integer, each x has a y, and these y values are necessary.
Group B: In the same way.
When the set A is not limited by X, the value that Y can get is greater than or equal to-1; When there is no limit to X in set B, the value that Y can get is less than or equal to 1, and there are not many * * * parts in the two sets. Now, X is required to be an integer, and the * * * part can be found by trying several numbers. Set A:- 1, 0, 3 ...; Set b: 1, 0, -3 ... and both * * * have only 0, so A∩B={0}
6. Subset: φ (symbol of empty set); { 1}; {2}; {3}; { 1,2}; { 1,3}; {2,3}; { 1,2,3};
Proper subset (not including its own set) {1,2,3}): φ (symbol of empty set); { 1}; {2}; {3}; { 1,2}; { 1,3}; {2,3};
Non-empty proper subset (except the set of proper subset empty sets): {1}; {2}; {3}; { 1,2}; { 1,3}; {2,3}
Analysis: Set A: An integer whose element is X and whose feature is greater than 0.
Set b: an integer greater than -2 and less than 4, namely-1, 0, 1, 2, 3.
So a ∩ b = {1, 2,3}, write a subset of this new set, proper subset and non-empty proper subset.
I don't know if it is detailed enough. I hope it helps you. ...