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: <em>"If a point lies outside a line, then exactly one plane contains both the line and the point".</em>
So, the statement "A line, and a point outside the line are in exactly one plane" holds true.
According to Plane Intersection Postulate: <em>"If two planes intersect, then their intersection is a line".</em>
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.
<em>Let </em><em>p </em><em>be the statement: </em>"A line, and a point outside the line are in exactly one plane". So, the statement p is true (T).
<em>Let </em><em>q</em><em> be the statement: </em>"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.
<h3>
p q p ∨ q
</h3>
T F T
So, T F → T illustrates the truth value of the given statements.
<em>Keywords: truth value, plane, line, intersection</em>
<em>learn more about truth values from brainly.com/question/9051197</em>
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