Answer true or false for each statement and give a logically valid explanation to support your...

Answer true or false for each statement and give a logically valid explanation to support your answer (you can give a counterexample if it is false, or make a proof if it is true).

a. The multiplication of two irrational numbers is an irrational number.

b. The set {( 1−n/ n , 8n+1/ n ) |n ∈ N } is an open covering of (−1, 8].

c. The sequence {( 1−3n /n + (−1)ⁿ ) |n ∈ N } has a sub-sequence that converges to -4.

d. The sum of the Lebesgue measure of the sets A = C ∪ [−5, 1), and B = Q ∩ [4, 10] is 6, where C is the Cantor ternary set, and Q is the rational numbers set.

e. Find the inf and sup of the set A = {x ∈ R : x ² − 4x ≤ 20 − 5x} are -5 and 4 respectively.

f. The intersection set for the following collection of intervals is open. {(−1/n − 2, 3 + 1/n), n ∈ N} .

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Expert Solution

Colby Messinger answered 1 year ago

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