let p: a shape is a triangle. let q: a shape has four sides. which is true if the shape is a rectangle? o…
let p: a shape is a triangle. let q: a shape has four sides. which is true if the shape is a rectangle? o p→q o p∧q o p↔q o q→p
Answer
Explanation:
Step1: Analyze the truth - values of p and q for a rectangle
A rectangle is not a triangle, so (p) (a shape is a triangle) is false. A rectangle has four sides, so (q) (a shape has four sides) is true.
Step2: Analyze each logical connective
- For (p\rightarrow q): A conditional statement (p\rightarrow q) is false when (p) is true and (q) is false, and true otherwise. Since (p) is false, (p\rightarrow q) is true.
- For (p\land q): A conjunction (p\land q) is true only when both (p) and (q) are true. Since (p) is false, (p\land q) is false.
- For (p\leftrightarrow q): A biconditional (p\leftrightarrow q) is true when (p) and (q) have the same truth - value. Since (p) is false and (q) is true, (p\leftrightarrow q) is false.
- For (q\rightarrow p): Since (q) is true and (p) is false, (q\rightarrow p) is false.
Answer:
(p\rightarrow q)