Logic and Proof Exercises

Give an example of the symmetric property.

Hint

Think of the symmetric property like a line of symmetry that you can flip things across.

If we're given a puppy, what property allows us to say that puppy = puppy?

Hint

Even though the puppy isn't a contortionist, the same property applies.

If ^A⁄_B = ^C⁄_D, which statements would make this true?

Hint

You should use the division property as long as you promise not to divide by zero.

If X = Y and Y = 3, which properties allow us to say that 3 = X?

Hint

We aren't adding, subtracting, multiplying, or dividing.

If A = B and X = Y, which properties allow us to say that ?

Hint

Assume that C ≠ 0. We don't want to go down that road.

If A = B, B = C, C = D, D = E, E = F, and F = G, which properties allow us to say that A(B + C) = DE + FG?

Hint

The statement is true. Which properties allow it?