Arguments: "Write the truth value for the following biconditional statement..."

[Zelda22]

I need help please. I can’t understand why my answers are not correct.



1. Write the truth value for the biconditional statement.

" A shape is a rectangle if and only if the shape has 4 sides."

I think the truth value is .

"If and only if" - both conditions must be true.

if p→q is true and
q→p is true, then p↔q

p→q If a shape is a rectangle, then the shape has 4 sides. TRUE
q→p If a shape has 4 sides, then the shape is a rectangle. FALSE
counterexample: a trapezoid has 4 sides but is NOT a rectangle.

Therefore, the biconditional statement must be False.

2. Write the truth value each statement.


a. If a shape is a rectangle, then it has four sides. TRUE
conditional p→q

b. If a shape has four sides, then it is a rectangle. FALSE
converse q→p
(counterexample: a trapezoid has 4 sides but is NOT a rectangle).

c. If a shape is not a rectangle, then it does not have four sides.
FALSE
inverse ∼p→∼q
(counterexample: a trapezoid is not a rectangle and has 4 sides).

d.If the shape has not four sides, then it is not a rectangle.
TRUE.
contrapositive ∼q→∼p

thank you

 

[blamocur]

I can’t understand why my answers are not correct.

I can't either. They look correct to me.

 

[Zelda22]

I can't either. They look correct to me.

Thank you.