Prove that if a,b belong R(Real Numbers) then |a|-|b| is lesser or equals to |a-b|

Q: 74. Prove that for any real numbers a and b, |b − a|=|a − b|.

A: Given; a and b are any real numbers Consider, L.H.S=b-aWe can write it as,=b+-a=-1-b+a=-1a-b…

Q: Prove: Let a > 0 and b > 0 then either a > 0 and b > 0 or a < 0 and b < 0. where a…

A:

Q: b) Prove that + ≥ 2, for any nonzero real numbers a and b.

A:

Q: Show that if both f: A ---> B and g: B ----> C are bijective, then g 0 f: A ---> C is bijective.

A:

Q: Let a,b,c,d be real number with a < b < c < d. Express the set [a,b] U [c,d] as the difference of…

A: We have given that, a, b, c, d are real numbers with a &lt; b &lt; c &lt; d. We need to express a, b…

Q: Prove that |ab|= |a | |b| for any numbers a and b.

A:

Q: Prove the following theorem using direct proof 1. For every pair of positive real numbers x and y,…

A:

Q: Show that if a < c< b, then fave (a, b) = () fave l(a, c) + C - a | favg [c, b]

A: Solution...

Q: For all real numbers a and b, |a + b| < ]a| + |bl. Select one: OTrue False

A: Answer

Q: Prove that a b + 2c + 3d + c+ 2d + 3a Let a, b, c, d be positive real numbers. C d + 2a + 3b + d a +…

A:

Q: Prove that la + b + c| < ]a] + ]b| + |c[

A: Prove that,    a+b+c≤a+b+c

Q: 1

A:

Q: 1 1. -to prove that x+y|# | x|+ | y| for all real numbers d) Use x = and y = %3D x and y.

A:

Q: Prove or disprove that ⌈x + y⌉ = ⌈x⌉ + ⌈y⌉ for all real numbers x and y.

A: According to the given information, It is required to prove or disprove that:

Q: Let a and b be non-negative real numbers with b+ 0 and p,q > 1 and+= 1, then a show that ab <+

A: Define a function y : [0,∞)→ℝ by yt=1q+tp-t1p, for every t∈ [0,∞). Now differentiating,…

Q: Let S = {-5,-1,0,2/3,5/6,1,sqrt(6),4,5} Determine which elements of S satisfy the inequality.…

A:

Q: Let r and s be nonnegative real numbers, f(r) = r" and g(r) = r. %3D Find all pairs r and s such…

A: Given that: f(x)=xr           and             g(x)=xs

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: Find a pair of values (x, y) that serve as a counter-example for the statement that [ry] : |x||y for…

A: The ceiling function gives smallest integer that is greater than the number, that is, x is the…

Q: 2. For all real numbers a, b and c, prove that if a <b <c then a+b+c a < 3 < C.

A: given that a, b, c are real numbers we have to prove that if      a&lt;b&lt;c    then…

Q: (c) Prove that x - 11 |x| + 11 |x² + 36| 36 for all real r.

A:

Q: Let x and y be real numbers. Disprove: If |x| < |y| then |x+1|< |y+1]. Let x, y, and z be real…

A:

Q: What does the set of real numbers consist of?

A: To discuss about real number

Q: Show that ACB implies |A|≤|B|.

A:

Q: Give an example of numbers a and b such that |a + b| &lt; |a|+|b|.

A: To give an example of numbers a and b such that

Q: Which of the following defines the domain of |4x-8<12? A) -8<x<-4 B)-4 <x < 8 C) -1<x< 5 D) 1<x<5

A: We can solve the inequality in order to get the solution.

Q: Determine real numbers a and b such that |x+a|−b≤0 iff -4≤x≤12.

A: given  x+a-b≤0if -4≤x≤12

Q: What is the set R of all real numbers?

A: Real numbers are the numbers which include both rational and irrational numbers. A real number is a…

Q: Let x be a real number. Prove by contrapositive that if x + 5x = 40, then x < 3.

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.