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For two real numbers a and b, min(a, b) denotes the smaller of a and b; while max(a, b)

Chapter 3, Problem 27

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QUESTION:

For two real numbers a and b, min(a, b) denotes the smaller of a and b; while max(a, b) denotes the larger of a and b. So min(3, 5) = 3 and max(3, 5) = 5, while min(4, 4) = max(4, 4) = 4. For two real numbers a and b, let m = min(a, b) and M = max(a, b). Let r and s be real numbers. Prove that if \(r \leq m\), then \(r \leq a\) and \(r \leq b\); while if \(s \geq M\), then \(s \geq a\) and \(s \geq b\).

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QUESTION:

For two real numbers a and b, min(a, b) denotes the smaller of a and b; while max(a, b) denotes the larger of a and b. So min(3, 5) = 3 and max(3, 5) = 5, while min(4, 4) = max(4, 4) = 4. For two real numbers a and b, let m = min(a, b) and M = max(a, b). Let r and s be real numbers. Prove that if \(r \leq m\), then \(r \leq a\) and \(r \leq b\); while if \(s \geq M\), then \(s \geq a\) and \(s \geq b\).

ANSWER:

Step 1 of 3

For min(a, b) denotes smaller of a and b means here the value which is smaller is taken out.

If a is smaller than b then a is considered otherwise b is considered.

For max(a, b) the greater value is taken out if a is greater than b then a is considered otherwise b is taken out.

Therefore, In min(3, 5) = 3 so 3 is taken out and max(3, 5) = 5 is considered. 

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