Does changing the compound inequality x > - 3 and x < 3 from "and" to "or" change the solution set? explain.

Question

Mathematics

Angelica

2 January, 15:21

Does changing the compound inequality x > - 3 and x < 3 from "and" to "or" change the solution set? explain.

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Answers (2)

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Valery Mitchell · Answer 1

Yes. In interval notation:

x > - 3 and x < 3 = (-3, 3)

x > - 3 or x < 3 = (-inf, inf)

x > - 3 xor x < 3 = (-inf, - 3] U [3, inf) where xor is the "exclusive or", either-or but not both.

Makenzie Horton · Answer 2

Sure yes.

1) x > - 3 or x < 3 means that the solution set is all the numbers greater than - 3 and all the numbers smaller than 3. That is, this union of intervals: (-3,∞) U (-∞,3), which is all the real numbers.

2) x > - 3 and x <3 means that the solution set is the numbers that are at the same time greater than - 3 and smaller than 3. That is the intersection of the intervals: (-3,∞) ∩ (-∞,3), which is the interval (-3, 3).