Question

Does changing the compound inequality x > −3 and x < 3 from “and” to “or” change the solution set? explain.

Answer 1

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).

Answer 2

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.