Let x be a real number.
Which one of the following statements is a sufficient condition for exactly three of the other four statements?
- Ax ≥ 0
- Bx = 1
- Cx = 0 or x = 1
- Dx ≥ 0 or x ≤ 1
- Ex ≥ 0 and x ≤ 1
Show the answer and worked solution
answer · C
- Ax ≥ 0
- Bx = 1
- Cx = 0 or x = 1
- Dx ≥ 0 or x ≤ 1
- Ex ≥ 0 and x ≤ 1
Note first that "x ≥ 0 or x ≤ 1" holds for every real number. Take each option in turn. "x ≥ 0" implies only that one. "x = 1" implies all four of the others. "x ≥ 0 and x ≤ 1" implies two. And the always-true statement implies none of the restrictive ones. But "x = 0 or x = 1" implies x ≥ 0, the always-true statement, and 0 ≤ x ≤ 1 — exactly three — while leaving x = 1 open.