| A | B |
|---|
| Commutative Axiom of Addition | a + b = b + a |
| Commutative Axiom of Multiplication | ab = ba |
| Associative Axiom of Addition | (a + b) + c = a + (b + c) |
| Associative Axiom of Multiplication | (ab)c = a(bc) |
| Additive Identity Axiom | a + 0 = a |
| Additive Inverse Axiom | a + (-a) = 0 |
| Distributive Property (of multiplication with respect to addition) | a(b + c) = ab+ ac and (b + c)a = ba + ca |
| Multiplicative Identity Axiom | a(1) = a and 1(a) = a |
| Multiplicative Property of Zero | a(0) = 0 and 0(a) = 0 |
| Multiplicative Property of -1 | a(-1) = -a and (-1)a = -a |
| Multiplicative Inverse Axiom | a(1/a) = 1 and (1/a)a = 1 |
| Definition of Subtraction | a - b = a + (-b) |
| Definition of Division | a/b = a(1/b) |
| Communative Axiom for Addition | 4+x = x+4 |
| Commutative Axiom for Multiplication | p(mt) = p(tm) |
| Associative Axiom for Addition | 21+(-5)+7x = [21+(-5)]+7x |
| Associative Axiom for Multiplication | 5(3x) = (5x3)x |
| Additive Identity Axiom | 0+3t = 3t |
| Additive Inverse Axiom | 5+(-5)=0 |
| Multiplicative Identity Axiom | 2b x 1=2b |
| Multiplicative Inverse Axiom | 2k x 1/2k=1 |
| Multiplicative Property of -1 | -1(47n)= (-47n) |
| Multiplicative Property of Zero | 36 x 0 = 0 |
| Definition of Subtraction | 5x+13-2x = 5x+13+(-2x) |
| Definition of Division | 4f/f = 4f x 1/f |
| Transitive Axiom of Equality | If x=y and y=z, then x=z |
| Transitive Axiom of Equality | If x=2+3 and 2+3=5, then x=5 |
| Symmetric Axiom of Equality | If x=y, then y=x |
| Symmetric Axiom of Equality | If x=7, then 7=x |
| Symmetric Axiom of Equality | If x+6=8, then 8=x+6 |
| Reflexive Axiom of Equality | x=x |
| Reflexive Axiom of Equality | 5y=5y |
| Addition Property of Equality | If x=y, then x+z = y+z |
| Addition Property of Equality | If 3x+5=14, then 3x+5+ (-5 )= 14+ (-5) |
| Multiplication Property of Equality | If x=y, then xz=yz |
| Multiplication Property of Equality | If 7a=28, then 7a x (1/7) = 28 x (1/7) |
