Find the supremum of each of the following sets. (If the supremum is infinite, enter the word "infinity". If it is a real number, round it to 1 decimal place.) {1, 12,3} {(x - 2)² x ER, 0 < x < 1} : { = /2: "EN } n р +1 :p a prime number :} <

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A: Given function .Note: According to the guidelines we are allowed to solve three sub parts at a time.…

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A: We can find the answer as below.

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A: ANSWER :

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A: follow next step

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A:

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

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

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A: We write the statement of Archimedean Property and proof the given statement

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A: The factorial function tells us to multiply all whole numbers down to 1 from the selected number.