Answer:
T F → T illustrates the truth value of the given statements.
Step-by-step explanation:
According to Point and Line contained in Plane Theorem: "If a point lies outside a line, then exactly one plane contains both the line and the point".
So, the statement "A line, and a point outside the line are in exactly one plane" holds true.
According to Plane Intersection Postulate: "If two planes intersect, then their intersection is a line".
So, according to this postulate, two planes intersect in a plane is false.
Although two Planes in three-dimensional space are able to intersect in one of three ways:
- Two planes would only intersect in a plane if they are coincident.
- Two planes would never intersect if they are parallel.
- If the option 1 and 2 do not hold true, then the two planes would intersect in a line.
But, as it is not specified in the question that the planes were coincident, so we assume that two planes would intersect in a line. Hence, the statement "two planes intersect in a plane" is false.
Let p be the statement: "A line, and a point outside the line are in exactly one plane". So, the statement p is true (T).
Let q be the statement: "two planes intersect in a plane". So, the statement q is false (F).
Hence, the statement p or q is written as p ∨ q.
As p is true (T) and q is false (F), hence p ∨ q will be true (T).
i.e.
p q p ∨ q
T F T
So, T F → T illustrates the truth value of the given statements.
Keywords: truth value, plane, line, intersection
learn more about truth values from brainly.com/question/9051197
#learnwithBrainly
