Question

which statement is true about this argument?
premises:
if two lines are parallel, then the lines do not intersect.
lines m and n do not intersect.
conclusion:
lines m and n are parallel.
which statement is true about the argument?

the argument is not valid because the premises are not true.
the argument is valid by the law of syllogism.
the argument is not valid because the conclusion does not follow from the premises.
the argument is valid by the law of detachment.

Explanation:

The law of detachment requires the form "if p then q, p, so q". Here, we have "if p then q, q, so p" which is an invalid form called affirming the consequent. The conclusion does not follow from the premises. The first premise is a conditional statement and the second premise affirms the consequent of the conditional, but we cannot validly conclude the antecedent.

Answer:

The argument is not valid because the conclusion does not follow from the premises.