# Logic and Proof

# The Quality of Equality Exercises

### Example 1

Give an example of the symmetrical property.

### Example 2

If we're given a puppy, what can we say about the puppy and which property would we be using?

### Example 3

^{A}⁄_{B} = ^{C}⁄_{D}. Which statements would make this true?

### Example 4

*X* = *Y* and *Y* = 3. Which properties allow or forbid us to say that 3 = *X*?

### Example 5

*A* = *B* and *X* = *Y*. Which properties allow or forbid us to say that ?

### Example 6

*A* = *B*, *B* = *C*, *C* = *D*, and *D* = *E*, *E* = *F*, and *F* = *G*. Which properties allow or forbid us to say that *A*(*B* + *C*) = *D* × *E* + *F* × *G*?