Question

Which of these are true statements? The domain of all variables is the integers.

a.∀x∀y∀z(x(yz) = (xy)z)
b.∀x∀y∃z(x + y = z)

Answer 1

The true statement is a. ∀x∀y∀z(x(yz) = (xy)z). To show this, use the associative property of multiplication.

Step-by-step explanation:

The true statement is a. ∀x∀y∀z(x(yz) = (xy)z)

To show that this statement is true, we need to use the associative property of multiplication. According to this property, the way the parentheses are arranged does not change the result of the multiplication.

Let's use an example:

- Let x = 2, y = 3, and z = 4.

With the left side of the equation, we have (2(3*4)) = (2*12) = 24.

With the right side of the equation, we have ((2*3)*4) = (6*4) = 24.

As you can see, both sides of the equation yield the same result, proving that the statement is true.