1. The additive identity is 0. This is because adding 0 to anything leads to the same value. Example: 0+3 = 3.
2. An equation is where you have two expressions separated by an equal sign. In your case it would be "a mathematical sentence whose verb is 'equal' (=)"
3. The multiplicative identity is 1. Multiply 1 with any number and the result is that same number. Example: 1*7 = 7.
4. An open sentence is an equation that contains one or more variables. An example would be x+2 = 4. The reason why we call it open is because the true or false nature of the sentence is up in the air until we know what x is. If we knew that x = 3 for instance, then x+2 = 4 would be false since 3+2 = 4 is false. If we nailed down what x was then it would go from open to closed.
5. The symmetric property is that if a = b then b = a. Think of a mirror how the image reverses.