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Chapter 4: Problem 52

True or False \(y=y\)

Short Answer

Expert verified
Answer: False.

Step by step solution

01

Consider the inequality \(y < x\)

The inequality \(y < x\) means that the value of \(y\) is less than the value of \(x\). We will keep this in mind and check if the other inequality implies the same meaning.
02

Consider the inequality \(x \ge y\)

The inequality \(x \ge y\) means that the value of \(x\) is greater than or equal to the value of \(y\). Note that the "equal to" part is different from the first inequality.
03

Comparison of both inequalities

We can see that while both inequalities have a similar structure, the \(x \ge y\) inequality includes the possibility of \(x\) being equal to \(y\), whereas the inequality \(y < x\) does not allow for \(x\) and \(y\) to be equal.
04

Conclusion

Since the inequality \(x \ge y\) contains the possibility of \(x\) being equal to \(y\), and the inequality \(y < x\) does not allow for this case, the two inequalities are not the same. Therefore, the answer is False.

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