4) Consider the collection of intervals on the real line: B = { (a, b) | a < b and (b – a) > 1}. Is this a basis for a topology on R? If so, prove it. If not, explain why not.

Q: prove theorem: if a square is inscribed into a right triangle in such a way that one side of the…

A:

Q: Let H = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, f} Let W = {(a, b) : a € H, b = H} be the…

A: Answer:-

Q: Using R, use antithetic variables to estimate the following: 3 0 = Se -t²4 P7+1dt Note: For each of…

A: The antithetic variable method is a variance reduction technique used in Monte Carlo integration. It…

Q: What would be the degrees of freedom for a chi-square table that has an independent variable with 2…

A: Here given that independent variable with 2 groups and a dependent variable with 2 groups.

Q: . Show that if P(A) > 0, then P(AB|A) ≥ P(AB|A U B)

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Q: With each step show the rule associated with it

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Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: R² = gen gen

A: see below the reason

Q: |z+2i|=|z+1- 3i|

A:

Q: a and b are positive integers, show that gcd(a,b) = gcd(a,a+b).  Discrete math questio

A: To prove that gcd(a, b) = gcd(a, a + b) for positive integers a and b, you can use the properties of…

Q: If, (V₁ X V₂) · V3 = 6.5 then what is (V3 X V₁) - V₂? ○ (0,0,0) Cannot be found with the given…

A:

Q: 12 + 22,., +n? =n(n+ 1)(2n + 1), Vn eN

A: We will prove this as following.

Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

A:

Q: 7.1 12

A:

Q: Suppose a is divisible by b. Show that gcd(a, b) = b.

A: Consider the given information. As we have given that a is divisible by b. then there is a number c…