Question

Let p: A triangle is acute. Let q: A triangle is equilateral. If q is true, which statements must be true? Check all that apply.

a.p ∨ q
b.p ∧ q
c. p → q
c.q → p
d. q ↔ p

Answer 1

A statement is true if both p and q will be true.

As, given ,p: A triangle is acute

q: A triangle is equilateral.

p ∧ q→ p is true as well as q is true.

That is if triangle is acute it means it is equilateral is not possible, and if triangle is equilateral it means it is acute angled triangle.So,this contradicts p∧q.

So, Option (c) q → p, supports the two statement , that is if if triangle is equilateral it means it is acute angled triangle.

Answer 2

"q is true" is a given statement. So q = T where T stands for T (while F is for false)

If the triangle is equilateral, then all three angles are 60 degrees. So the triangle is also acute. This makes statement p true as well.

So p and q are both true logical statements.

That makes p v q true. It's only false if BOTH are false but that's not the case here.

That makes p ∧ q true as well. BOTH statements are true, so the entire thing is true.

p --> q is true as well. This is only false if p were true leading to q being false. Again not the case.

In the other direction, q --> p is also true for similar reasons as the last explanation above.

q <--> p is true because p and q have the same truth value T

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In summary, every choice is true.