Principles of the Algerbra of Logic
Principles of the Algerbra of Logic
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The latter examples differ from the former in that the equivalence asserted does not involve identity.
Observation. — The equation xy^x+y—i is an equation of Condition ; whereas the equation xy=x+y'-i+{i'-x)(i''y) is an Identity. _ 204. Jfxy=m, then xy=m; but not conversely.
For xy=m expresses the identity of the IPs which are x and^ with those which are m. Hence the arithmetical value of xy must be equal to that of m ; that is, xy=m.
But suppose it is given that xys=m.
Digiti ized by Google of... the form xy^nt. ( Hypothetical.) 83 Since xy may in general have the quantitative value m in a pliurality of ways, and xy^m is only one of these ways ; it does not follow that xy^m.
Cor. If xy^x^ then xy=x.
For xy can have the quantitative value x in only one way; and xy=sx is one way.
205. Hhere are ctriain forms of the eqtuition xy^m, which can be satisfied only by one or both of the symbols having a singular value.
First example ; :cy = i — ;c.
Then xy+x=iy .•. xy=Of (Art. 136) for i is single.
What to read after Principles of the Algerbra of Logic?
You can find similar books in the "Read Also" column, or choose other free books by Alexander Macfarlan to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The latter examples differ from the former in that the equivalence asserted does not involve identity.
Observation. — The equation xy^x+y—i is an equation of Condition ; whereas the equation xy=x+y'-i+{i'-x)(i''y) is an Identity. _ 204. Jfxy=m, then xy=m; but not conversely.
For xy=m expresses the identity of the IPs which are x and^ with those which are m. Hence the arithmetical value of xy must be equal to that of m ; that is, xy=m.
But suppose it is given that xys=m.
Digiti ized by Google of... the form xy^nt. ( Hypothetical.) 83 Since xy may in general have the quantitative value m in a pliurality of ways, and xy^m is only one of these ways ; it does not follow that xy^m.
Cor. If xy^x^ then xy=x.
For xy can have the quantitative value x in only one way; and xy=sx is one way.
205. Hhere are ctriain forms of the eqtuition xy^m, which can be satisfied only by one or both of the symbols having a singular value.
First example ; :cy = i — ;c.
Then xy+x=iy .•. xy=Of (Art. 136) for i is single.
What to read after Principles of the Algerbra of Logic?
You can find similar books in the "Read Also" column, or choose other free books by Alexander Macfarlan to read onlineMoreLess
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