Question

what conclusion can be drawn from the given statements by using the law of syllogism? given: if two lines are perpendicular, then they intersect to form right angles. lines s and r form right angles. choose the correct answer. a) lines s and r are perpendicular. b) if two lines form right angles, then they are perpendicular. c) any pair of lines are perpendicular. 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 \(p
ightarrow r\). Here the first statement is "If two lines are perpendicular, then they intersect to form right - angles" (\(p = \text{two lines are perpendicular}\), \(q=\text{they intersect to form right angles}\)). The second statement is "Lines \(s\) and \(r\) form right angles" which is just a statement about lines \(s\) and \(r\) forming right angles. The conclusion (\(q\)) of the first statement is not the hypothesis of the second statement. So no valid conclusion can be drawn using the Law of Syllogism.

Answer:

D. No valid conclusion can be drawn. The conclusion of the first statement is not the hypothesis of the second statement.