Let Z be the set of all integers and Q be the set of all rational numbers and R be the set of all real numbers, A=(20, 100], B (90, 150], C {70, 100, 200}, D (10, 30) and E= {x € Z: x=7 (mod 10)}. Find: (1) (Z-Q) and specified in it using the most concise notation. (ii) (A-(D-B)) specified using interval notation. (iii) ((A-B)UC-D) specified using set builder notation without any word (iv) The power set P(C) of C by listing down the elements directly. (v) (E-A) specified using the most concise set builder notation without any word.

Q: Select two positive integers a and b with 5 <  a  ≤  20  and 5  <  b ≤  20.

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Q: Is it possible to raise a positive number b to a power and obtain a negative number? Is it possible…

A: The given statement is " The possibility to raise a positive number b to a power and obtain a…

Q: Does the symbol for infinity (q) represent a real number?

A: Yes, the symbol for infinity (∞) represents a real number.  Infinity (∞) means a very big number.…

Q: Derive one-one correspondence between the real numbers in (0,1) and the set of irrational numbers in…

A: Both the sets that is real number in 0,1 and the set of irrational numbers in 0,1 are uncountable as…

Q: If a,b,c,d are in distinct real number in A.P. Such that 2(a-b)+c(b-c) +(c-a) =2(a-d)+(b-d) +(c-d)'…

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Q: Prove that a number in the form 6k+5,” what I mean is a number in the form of 6 times some integer…

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Q: Given any real numbers a and d, consider the expression (a + md) + (a + (m + 1)d) + (a + (m + 2)d) +…

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Q: Prove that 1+6x-x is always a positive real number if x =3+Ai for some real 33 number 4

A: The given number is  1 + 6x - x2

Q: FIND AUB,GIVEN THAT A= {x/x is a positive integer. 2<x<6}    B= {x/x is a negative integer, - 6<x<…

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Q: Suppose a and b are positive real numbers and n is a natural number with n 2 2. (a) Use the…

A: Let a and b are positive real numbers and n is a natural number with n≥2. Use the difference of…

Q: sing direct proof, prove the following statements: 1. Prove: If x2-4=0, then x = 2 or x = -2. 2. If…

A: follow next step

Q: A) (1 + √₂)² B) (1 -√2)² c)(1+√2)(1+√-2) D)(1+√2)(1-√√2) E)√2² + (√2)² Which of the above…

A: A) 1+22B) 1-22C) 1+21+2D) 1+21-2E) 22+22

Q: Disprove the statement: There is a real number x such that xº +x* +1 = 2x².

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Q: Show that x2 + 9 is prime.

A: To show x2 + 9 is prime.

Q: Find all the values of x such that X 4²x17 * 4 + 16 = 0

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Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: Use proof by contradiction to show that there is no positive real number x such that (x-2)/x ≥…

A: In an inequality, if a positive number is multiplied then there is no change of sign of inequality.…

Q: For non-zero denominators, which of the following is equivalent to 1 2a a a + 1 -2a3 +1 a(a + 1) 1-…

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Q: Find an odd integer o written as an expression using the variable k with the property that when f is…

A: Here we have given a mapping  which proves that both the sets have same cardinality.

Q: So what's the final value of x1 x2 x3 and x4? indivually

A: Answer :  No value  the system of equations does not converge to any value. so there doesn't exist…

Q: 7 [3-(2-5x)] + X= 4 (9x+2} +1+x/²

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Q: If [5 - -8 A = [611] 0 " then A- 1 =

A: The objective of the question is to find the value of 'A - 1' given the equation '5 - -8A = 611'.

Q: Show that V3 +2/6 is an irrational number.

A: A rational number can be represented as pq, where p, q are integers and q≠0. If a number can not be…

Q: How many integer solutions to x1+ x2+ x3+ x4 = 36 are there for which æ1 > 5, x2 > 3, x3 > 5 and æ4…

A: We have to find the number of solutions to x1+x2+x3+x4=36 for which x1≥5, x2≥3, x3≥5 &amp; x4≥6.