Question

If p represents "Triangle ABC is right" and a represents "Triangle ABC has a right angle."Which of the following represents the argument presented below?"Triangle ABC is right if and only if Triangle ABC has a right angle.""Triangle ABC is right or Triangle ABC has a right angle.""Therefore, Triangle ABC is right and Triangle ABC has a right angle."

Answer 1

Step 1: Write out the statement

p is the statement "Triangle ABC is right"

q is the statement "Triangle ABC has a right angle"

Step 2: Write out the representations of the arguments

The symbol for "if and only if" is ⇔

Therefore the representation for the statement

"Triangle ABC is right if and only if Triangle ABC has a right angle." is

p ⇔ q

The symbol for "or" is ∨

Therefore the representation for the statement

"Triangle ABC is right or Triangle ABC has a right angle." is

p ∨ q

The symbol for "Therefore" is ∴

and the symbol for "and" is ∧

Therefore the representation for the statement

"Therefore, Triangle ABC is right and Triangle ABC has a right angle." is

∴(p ∧ q)

s