Question

Which of the following represent the addition property of equality?

If a = b and c = d, then ac = bd.
If a = b and c = d, then a + b = c + d.
If a = b and c = d, then a + c = b + d.
If a = b and c = d, then ac + b = bd + a.

Answer 1

Only the third:

- If a = b and c = d, then a + c = b + d. (This is the addition property: adding equals gives equals.)

Notes on the others:
- (1) is a multiplication property (or follows by multiplying the equalities).
- (2) is generally false (e.g. a=b=1, c=d=2 gives a+b=2 but c+d=4).
- (4) is true as a consequence (substitute b=a and d=c to get ac+b = ac+a), but it is not the basic addition property—it's a combination of substitution and multiplication/addition.