Consider the proposition: “If the pressure increases, the volume decreases. The negation of this proposition is

Question

Consider the proposition: “If the pressure increases, the volume decreases. The negation of this proposition is (A) If the pressure does not increase the volume does not decrease (B) If the volume increases, the pressure decreases (C) If the volume does not decreases, the pressure does not increase (D) If the volume decreases, then the pressure does not increase

Tardigrade Admin · Accepted Answer

We know that p arrow q ≅ ∼ q arrow ∼ p So, the given statement is equivalent to: If the volume does not decrease, the pressure does not increase

Q. Consider the proposition: “If the pressure increases, the volume decreases. The negation of this proposition is

If the pressure does not increase the volume does not decrease

If the volume increases, the pressure decreases

If the volume does not decreases, the pressure does not increase

If the volume decreases, then the pressure does not increase

We know that $p \to q ≅\sim q \to\sim p$
So, the given statement is equivalent to:
If the volume does not decrease, the pressure does not increase

Q. Consider the proposition: “If the pressure increases, the volume decreases. The negation of this proposition is

If the pressure does not increase the volume does not decrease

If the volume increases, the pressure decreases

If the volume does not decreases, the pressure does not increase

If the volume decreases, then the pressure does not increase

We know that p→q≅∼q→∼p So, the given statement is equivalent to: If the volume does not decrease, the pressure does not increase

We know that $p \to q ≅\sim q \to\sim p$
So, the given statement is equivalent to:
If the volume does not decrease, the pressure does not increase