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A set problem in high school mathematics It is known that M = {x | - 2 less than or equal to x less than or equal to 5}, n = {x | - A + 1 less than or equal to x less than or equal to 2a-1} 1. If M is contained in N, find the value range of real number a 2. If n is contained in M, find the value range of real number a
1, - 2 ≥ a + 1 and 5 ≤ 2a-1
There is no solution for a
2, a + 1 ≥ - 2 and 2a-1 ≤ 5
∴a∈[-3,3]
12. Let a be a nonempty subset of an integer set. For K belonging to a, if k-1 does not belong to a, and K + 1 does not belong to a, then K is said to be an "isolated element" of A. given s = (1,2,3,4,5,6,7,8), all sets composed of three elements of s have the same set without "isolated element"_____________ One
According to the meaning of the title, the element that is not adjacent to it is "isolated element", so "no isolated element" refers to the element that is adjacent to K in the set
Therefore, there are six sets in accordance with the meaning of the question: {1,2,3}, {2,3,4}, {3,4,5}, {4,5,6}, {5,6,7}, {6,7,8}
So the answer is: 6. Comments: this question mainly tests reading and understanding, information transfer and students' learning potential, and tests students' ability to analyze and solve problems. It belongs to the innovative type
When enumerating, we should have certain rules. We can start from one end, so as to avoid repetition and omission
High school mathematics problems ~ about set
Are there equal sets in the following sets? Try to explain
A=｛x‖y=x^2 -1 ｝ ; B=｛y‖y= x^2 -1｝；
C=｛(x,y) ‖ x^2 -1｝;D=｛ y=x^2 -1 ｝
The element in a is x, which refers to the definition field of the function y = x ^ 2 - 1. The element in a = RB is y, which refers to the range of the function y = x ^ 2 - 1. The element in B = {y | y ≥ - 1} C is (x, y), which refers to the set of all the points on the image of the function y = x ^ 2 - 1. It is a set of points, not a set of numbers
RELATED INFORMATIONS
- 1. Set a = {x | X & sup2; - 3x + 2 = 0}, B = {x | X & sup2; + 2 (a + 1) x + A & sup2; - 5 = 0} (1) If a ∩ B = {2}, find the value of A (2) If a ∪ B = a, find the value range of A (3) If u = R, a ∩ (cub) = a, find the value range of real number a
- 2. Given that P is equal to {0,1}, P is a set or an element
- 3. The set of positive integers divided by 5 and 2 is expressed as
- 4. Let a = {(x, y) / y = x ^ 2}, B = {(x, y) / y = 2 ^ x}, then the number of subsets a intersects B ()
- 5. Given the set a = {(x, y) y = f (x), X belongs to [a, b]}, B = {(x, y) x = 1}, then the number of elements contained in a intersection B is?
- 6. Given the function f (x) = AX2 + BX + C, f (- 3) = f (1) = 0, f (0) = - 3, we can find the solution set of the equation f (x) = 2x
- 7. Why to find the increasing interval of logarithmic function is to find the decreasing interval of compound function
- 8. The known function f (x) = ax & # 178; - x + 2a-1 If a > 0, let g (a) be the minimum value of F (x) in the interval [1.2]
- 9. It is known that the functions f (x) = asin (KX + π / 3) and φ (x) = btan (KX - π / 3), k > 0, and a; B belong to R. the sum of the minimum positive periods of the two functions is 3 π / 2, and f (π / 2) = φ (π / 2), f (π / 4) = - √ 3 φ (π / 4) + 1, find the analytic expressions of two functions
- 10. When k is the value, the domain of the function y = LG (KX ^ 2 + 4kx + 3) is r? When k is the value, the domain is r?
- 11. Decomposition factor (AX by) & sup3; + (by CZ) & sup3; - (AX CZ) & sup3;
- 12. +By = 7, a times the square of X + B times the square of y = 49, a times the third power of X + B times the third power of y = 133, a times the fourth power of X + B times the fourth power of y = 406 Try to find the value of: 1995 (x + y) + 6xy-17 / 2 (a + b) + 4
- 13. Take any point P on the triangle ABC, record the distances from P to three sides a, B, C as X, y, Z in turn, and prove that AZ + by + CZ is the fixed value
- 14. Solve the equations AX = by = CZ = 1 / x + 1 / y + 1 / Z, where a > 0, b > 0, C > 0
- 15. Solve the problem a + B + C = 1 x + y + Z = 9 and find the maximum value of T = ax + by + CZ
- 16. If a > b > C and x > y > Z, how to prove ax + by + CZ > ay + BZ + CX?
- 17. Decomposition factor: (AX by) ^ 3 + (by CZ) ^ 3 + (CZ ax) ^ 3
- 18. The square plus ax minus B of the quadratic equation x with real coefficients is equal to zero, one root is between (0,1), one root is between (1,2), and a (0,2) 2) P (a, b), find the value range of the module of 0A vector multiplied by 0P vector △ 0P vector
- 19. F (x) = ax + 1 / a (1-x), where a is greater than 0, let g (a) be the minimum value of F (x) when 0 is less than or equal to X and less than or equal to 1 (1) Find the analytic expression of G (a); (2) find the maximum value of G (a) f(x)=ax+(1-x)/a
- 20. Let a, B, x, y belong to R, and a ^ 2 + B ^ 2 = 1, x ^ 2 + y ^ 2 = 1, prove that the absolute value of AX + by is less than or equal to 1 In addition to using the mean inequality, there are other solutions