Proofs

Example 1

Proof -(-5)=5 with the axioms and defintions.
Write these steps: Think these reasons:
Use law 3. a+0=a This axiom is a good start. Next use law 5 to create -(-5)).
Replace expression 0 with -5+(-(-5)). a+(-5+(-(-5)))=a Next replace a by 5.
Replace expression a with 5. 5+(-5+(-(-5)))=5 Next associate 5 and -5 with law 7.
Replace expression 5+(-5+(-(-5))) with (5+(-5))+(-(-5)). (5+(-5))+(-(-5))=5 Next evaluate 5+(-5) with law 5.
Replace expression 5+(-5) with 0. 0+(-(-5))=5 Next commute 0 and (-(-5)) with law 1.
Replace expression 0+(-(-5)) with (-(-5))+0. (-(-5))+0=5 Next evaluate the addition of 0 with law 3.
Replace expression (-(-5)) with law 3. -(-5)=5 Next indicate that the proof is completed.
Underline the answer.




Example 2

Proof x+1=1+x with the axioms and defintions.
Write these steps: Think these reasons:
Use law 1. a+b=b+a This axiom is a good start, because is has the same operation and the same order of variables. Next we replace the variables.
Replace expression a with x. x+b=b+x Next replace b with 1.
Replace expression b with 1. x+1=1+x Indicate that this is the answer.
Underline the answer.





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