Question

what conclusion can be drawn from the given statements by using the law of syllogism? given: if two lines in a plane are not parallel, then they intersect. if two lines intersect, then they intersect in a point. choose the correct answer. a) if two lines intersect in a point, then they are not parallel. b) if two lines intersect in a point, then they are in the same plane. c) if two lines in a plane are not parallel, then then they intersect in a point. d) no valid conclusion can be drawn. the conclusion of the first statement is not the hypothesis of the second statement.

Explanation:

Step1: Recall Law of Syllogism

The Law of Syllogism states that if \(p
ightarrow q\) and \(q
ightarrow r\), then \(p
ightarrow r\).

Step2: Identify statements

Let \(p\) be "two lines in a plane are not parallel", \(q\) be "they intersect", and \(r\) be "they intersect in a point".

Step3: Apply Law of Syllogism

We have \(p
ightarrow q\) and \(q
ightarrow r\), so \(p
ightarrow r\), which is "If two lines in a plane are not parallel, then they intersect in a point".

Answer:

C. If two lines in a plane are not parallel, then they intersect in a point.