Question

Which conclusion can be drawn based on the true statements shown? If a line segment is a diameter, then it is the longest chord in a circle. Line segment AB is a diameter. Based on the law of syllogism, line segment AB is the longest chord in a circle. Based on the law of detachment, line segment AB is the longest chord in a circle. Based on the law of syllogism, the longest chord in a circle is a diameter. Based on the law of detachment, the longest chord in a circle is a diameter.

Answer 1

Which conclusion can be drawn based on the true statements shown?

We have been given two true statements.

Statement 1: "If a line segment is a diameter, then it is the longest chord in a circle."

Statement 2: "Line segment AB is a diameter."

now we have to identify which of the following option, best describes the conclusion.

We see that Statement 1 contains two statements in "If P then Q form".

While Statement 2 is "P" form

Law of syllogism says "if a = b and b = c then, a = c." But we don't see such structure in given statements.

Hence answer will be law of detachment which says "If p then q is true, P is true then q must be true"

which matches with choice 2 is correct.

Hence final answer will be "Based on the law of detachment, line segment AB is the longest chord in a circle."