gaokao 2020 Q16

gaokao · China · national-II-science 5 marks Proof True/False Justification
Consider the following four propositions:
$p _ { 1 }$ : Three lines that are pairwise intersecting and do not pass through the same point must lie in the same plane.
$p _ { 2 }$ : Through any three points in space, there is exactly one plane.
$p _ { 3 }$ : If two lines in space do not intersect, then these two lines are parallel.
$p _ { 4 }$ : If line $l \subset$ plane $\alpha$ and line $m \perp$ plane $\alpha$ , then $m \perp l$ .
The sequence numbers of all true propositions among the following statements are $\_\_\_\_$.
(1) $p _ { 1 } \wedge p _ { 4 }$
(2) $p _ { 1 } \wedge p _ { 2 }$
(3) $\neg p _ { 2 } \vee p _ { 3 }$
(4) $\neg p _ { 3 } \vee \neg p _ { 4 }$
Consider the following four propositions:

$p _ { 1 }$ : Three lines that are pairwise intersecting and do not pass through the same point must lie in the same plane.

$p _ { 2 }$ : Through any three points in space, there is exactly one plane.

$p _ { 3 }$ : If two lines in space do not intersect, then these two lines are parallel.

$p _ { 4 }$ : If line $l \subset$ plane $\alpha$ and line $m \perp$ plane $\alpha$ , then $m \perp l$ .

The sequence numbers of all true propositions among the following statements are $\_\_\_\_$.

(1) $p _ { 1 } \wedge p _ { 4 }$

(2) $p _ { 1 } \wedge p _ { 2 }$

(3) $\neg p _ { 2 } \vee p _ { 3 }$

(4) $\neg p _ { 3 } \vee \neg p _ { 4 }$