- #1
evagelos
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Given 4 axioms in real Nos:
1) 1x = x ,for all x
2) x+0 = x ,for all x
3) (x+y)z = xz+yz ,for all x,y,z
4) xy =yx ,for all x,y
The cancellation theorem : [tex]\forall[x+y = x+z\Longrightarrow y=z][/tex]
And two laws of logic:
1) The law of Universal Elimination
2) The law of substitution.
Can we create a theorem?.
If yes ,what that theorem may be??
1) 1x = x ,for all x
2) x+0 = x ,for all x
3) (x+y)z = xz+yz ,for all x,y,z
4) xy =yx ,for all x,y
The cancellation theorem : [tex]\forall[x+y = x+z\Longrightarrow y=z][/tex]
And two laws of logic:
1) The law of Universal Elimination
2) The law of substitution.
Can we create a theorem?.
If yes ,what that theorem may be??