Question

In the Law of Syllogism, suppose pq and q- r are true, where p is "a polygon has three sides," q is "a polygon is a triangle," and r is "the interior angles of a polygon sum to 180°." If the truth value of p is T, what is the truth value of r?

a) T
b) F
c) Cannot be determined
d) Depends on the type of polygon

Answer 1

The truth value of 'r' is true (T), as the Law of Syllogism supports the logical deduction that a three-sided polygon must be a triangle, whose angles sum to 180°. option A is correct.

Step-by-step explanation:

In the Law of Syllogism, if 'pq' and 'q- r' are true, and if 'p' is the statement 'a polygon has three sides,' 'q' is 'a polygon is a triangle,' and 'r' is 'the interior angles of a polygon sum to 180°,' then the truth value of 'p' being true (T) does indeed guarantee that 'r' is also true (T).

Here we infer that since a three-sided polygon (p) is by definition a triangle (q), and a triangle (q) has interior angles that sum to 180° (r), then a polygon having three sides (p) necessarily leads to the interior angles summing to 180° (r). This logical deduction is based on the reliable nature of mathematical postulates and logical reasoning.