Question

Which of the following illustrates the truth value of the following statements?

Answer 1

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:

1. Two planes would only intersect in a plane if they are coincident.
2. Two planes would never intersect if they are parallel.
3. 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

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