Question

Let the domain be all triangles, let P(x)=x is equilateral and let Q(x)=x does not have a right anglc. Consider the statement: (∀x)(P(x)→Q(x)). i) Translate the statement into plain English

Answer 1

The logical statement translates to 'For every triangle, if it is equilateral, then it does not have a right angle,' affirming that equilateral triangles cannot have right angles.

Step-by-step explanation:

The statement (∀x)(P(x)→Q(x)) when translated into plain English means: "For every triangle, if the triangle is equilateral, then it does not have a right angle." This logical statement asserts that all equilateral triangles, by definition, will not contain a right angle. This is true because an equilateral triangle has three equal angles that each measure 60 degrees, and therefore none of the angles can be 90 degrees, which is required for a right angle.